A319575 a(n) = (2/3)*n*(n^3 - 6*n^2 + 11*n - 3).

0, 2, 4, 6, 24, 90, 252, 574, 1136, 2034, 3380, 5302, 7944, 11466, 16044, 21870, 29152, 38114, 48996, 62054, 77560, 95802, 117084, 141726, 170064, 202450, 239252, 280854, 327656, 380074, 438540, 503502, 575424, 654786, 742084, 837830, 942552, 1056794, 1181116

Offset: 0

Author

Peter Luschny, Oct 01 2018

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), this sequence (m=4), A319576 (m=5), A319577 (m=6).

Column n=4 of A122141.

Cf. A319574.

Programs

Maple

a := n -> (2/3)*n*(n^3 - 6*n^2 + 11*n - 3):
seq(a(n), n=0..38);

Mathematica

A319575[n_] := 2/3*n*(n^3-6*n^2+11*n-3); Array[A319575, 50, 0] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 4, 6, 24}, 50] (* Paolo Xausa, Feb 20 2024 *)

PARI

concat(0, Vec(2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Oct 02 2018

Formula

a(n) = [x^4] JacobiTheta3(x)^n.

a(n) = A319574(n,4).

From Colin Barker, Oct 02 2018: (Start)

G.f.: 2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End)