Sign up to save your podcasts
Or
Share OEIS A000338: Expansion of x^3*(5-2*x)*(1-x^3)/(1-x)^4
Share to email
Share to Facebook
Share to X
Share to email
Share to Facebook
Share to X
Or
OEIS A000338: Expansion of x^3*(5-2*x)*(1-x^3)/(1-x)^4
In this Deep Dive we unpack OEIS A000338. We explore its generating function, explain what the offset (offset 3, 1) means, and show how the infinite power-series expansion yields the sequence beginning 5, 18, 42, 75, 117. We derive the linear recurrence and connect the terms to a combinatorial story about discordant permutations, as discussed in J. Reordan's 1954 work and traced back to N. J. Sloan’s 1973 Handbook of Integer Sequences. The episode illustrates how a compact algebraic form hides a rich mathematical landscape of counting with forbidden positions.
Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.
Sponsored by Embersilk LLC
View all episodes
By Mike BreaultIn this Deep Dive we unpack OEIS A000338. We explore its generating function, explain what the offset (offset 3, 1) means, and show how the infinite power-series expansion yields the sequence beginning 5, 18, 42, 75, 117. We derive the linear recurrence and connect the terms to a combinatorial story about discordant permutations, as discussed in J. Reordan's 1954 work and traced back to N. J. Sloan’s 1973 Handbook of Integer Sequences. The episode illustrates how a compact algebraic form hides a rich mathematical landscape of counting with forbidden positions.
Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.
Sponsored by Embersilk LLC