The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A285551 Volume of each square prism building the next 3-dimensional box in A100538 where side lengths form the Padovan spiral number sequence (A134816), starting with 1 X 1 X 1, 1 X 1 X 2, 2 X 2 X 2, 2 X 2 X 3, 4 X 4 X 5, ... 2
 1, 2, 8, 12, 36, 80, 175, 441, 972, 2304, 5376, 12348, 29008, 67081, 156065, 363350, 843144, 1962396, 4560200, 10600000, 24648975, 57288465, 133194600, 309636096, 719790336, 1673379352, 3890033728, 9043304417, 21023197601, 48872682810, 113615800200, 264124052396 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Robert Dickau, Padovan's Spiral Numbers, Wolfram Demonstrations Project Published: August 19, 2010. Index entries for linear recurrences with constant coefficients, signature (1,2,3,-2, 4,-4,-1,-1,0,-1). FORMULA a(n) = A000931(n+5)^2*A000931(n+6). a(n) = A100538(n+1) - A100538(n). MATHEMATICA A[n_]:=Sum[Binomial[k, n - 2k], {k, 0, Floor[n/2]}]; a000931[n_]:=If[n==0, 1, If[n<3, 0, A[n - 3]]]; a[n_]:=a000931[n + 5]^2*a000931[n + 6]; Table[a[n], {n, 0, 50}] (* Indranil Ghosh, Apr 26 2017 *) LinearRecurrence[{1, 2, 3, -2, 4, -4, -1, -1, 0, -1}, {1, 2, 8, 12, 36, 80, 175, 441, 972, 2304}, 40] (* Vincenzo Librandi, Jul 19 2017 *) PROG (PARI) A(n) = sum(k=0, n\2, binomial(k, n - 2*k)); a000931(n) = if(n==0, 1, if(n<3, 0, A(n - 3))); a(n) = a000931(n + 5)^2*a000931(n + 6); \\ Indranil Ghosh, Apr 26 2017 (Python) from sympy import binomial def A(n): return sum([binomial(k, n - 2*k) for k in range(int(n/2) + 1)]) def a000931(n): return 1 if n==0 else 0 if n<3 else A(n - 3) def a(n): return a000931(n + 5)**2*a000931(n + 6) # Indranil Ghosh, Apr 26 2017 CROSSREFS Cf. A000931, A100538, A134816. Sequence in context: A062290 A176961 A078541 * A143231 A104039 A135443 Adjacent sequences: A285548 A285549 A285550 * A285552 A285553 A285554 KEYWORD nonn AUTHOR Peter M. Chema, Apr 25 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)