A264853 a(n) = n*(n + 1)*(5*n^2 + 5*n - 4)/12.

0, 1, 13, 56, 160, 365, 721, 1288, 2136, 3345, 5005, 7216, 10088, 13741, 18305, 23920, 30736, 38913, 48621, 60040, 73360, 88781, 106513, 126776, 149800, 175825, 205101, 237888, 274456, 315085, 360065, 409696, 464288, 524161, 589645, 661080, 738816, 823213, 914641

Offset: 0

Author

Ilya Gutkovskiy, Nov 26 2015

Keywords

• nonn
• easy

Comments

Partial sums of centered 10-gonal (or decagonal) pyramidal numbers.

Subsequence of A204221. In fact, a(n) is of the form (k^2-1)/15 for k = 5*n*(n+1)/2-1. - Bruno Berselli, Nov 27 2015

Links

• OEIS Wiki, Figurate numbers
• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A004466 (first differences), A201106 (partial sums), A204221.

Cf. similar sequences listed in A264854.

Programs

Magma

[n*(n+1)*(5*n^2+5*n-4)/12: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015

Mathematica

Table[n (n + 1) (5 n^2 + 5 n - 4)/12, {n, 0, 50}]
LinearRecurrence[{5,-10,10,-5,1},{0,1,13,56,160},40] (* Harvey P. Dale, Aug 14 2017 *)

PARI

a(n)=n*(n+1)*(5*n^2+5*n-4)/12 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: x*(1 + 8*x + x^2)/(1 - x)^5.

a(n) = Sum_{k = 0..n} A004466(k).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015