Questo è un episodio speciale che le classi 3A e 3B hanno dedicato ai loro nonni

Number of the Day - "364" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We dive into A000350, the Fibonacci-ending-in-M problem across bases. In base 10, there are many nontrivial M, suggesting rich, infinite variation. In binary, the situation collapses: only M = 0, 1, 5 work—a result finally proven by Max Alexei after extensive computation (up to M < 2^25). We trace the history back to mid-1960s Fibonacci Quarterly work and pose questions about other bases like base 3 or base 8, illustrating how changing the base reshapes the underlying number-theoretic land...

Number of the Day - "363" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Podcast sobre planificación automática

A dive into the niche OEIS sequence A000347, which counts partitions of integers into sums of non-integral powers. From A4 = 1 and rapid growth thereafter, the counting can be reformulated as counting ordered quadruples of positive integers x1 ≤ x2 ≤ x3 ≤ x4 with sqrt(x1) + sqrt(x2) + sqrt(x3) + sqrt(x4) ≤ n. We’ll trace the combinatorial setup, explain why the increasing order avoids duplicates, discuss the 2009 Manthar equivalence to the inequality counting problem, and explore the physics ...

Number of the Day - "362" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

angelo

A quick Deep Dive into A000346, defined as the Catalan numbers convolved with powers of 4. We explore its clean closed form, generating function, and the multiple combinatorial faces—Dyck paths, symmetric functions, and integer compositions—and what these connections reveal about growth and recurrence structure. Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information. Sponsored by Embersilk LLC

Number of the Day - "361" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Galois, mathématicien révolutionnaire

Number of the Day - "360"This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

A000344 counts a surprising blend of combinatorics and algebra. It arises as the number of lattice paths from (0,0) to (n,n) that touch but never cross the line x - y = 2 (i.e., stay on or below x - y = 2), which is the 5-fold convolution of the Catalan numbers. Equivalently, it tallies standard Young tableaux of shape (n+2, n, 2), and its ordinary generating function is A(z) = z^2 C(z)^5, where C(z) is the Catalan generating function. We’ll sketch the combinatorial picture, connect to the 5-...

Number of the Day - "359" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Number of the Day - "358" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

We explore A000342, the OEIS entry that counts n-node rooted trees of exact height 5. Height here means the longest path from the root to a leaf is exactly 5 edges, which forces at least 6 nodes. So the early terms start 0, 0, 0, 1, 5, 19, 61, illustrating how the height constraint shapes the counts compared with unconstrained rooted trees. We’ll discuss the counting machinery—recurrences, generating functions, and dynamic programming—and how these counts relate to other related problems in c...

ANGELO ci dara' i numeri....

Number of the Day - "357" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices

Number of the Day - "356" This podcast is produced by Klassic Studios. Check out our other podcasts there! Learn more about your ad choices. Visit megaphone.fm/adchoices