A155121 a(n) = 2*n*(1 + n + n^2 + n^3) - 3.

-3, 5, 57, 237, 677, 1557, 3105, 5597, 9357, 14757, 22217, 32205, 45237, 61877, 82737, 108477, 139805, 177477, 222297, 275117, 336837, 408405, 490817, 585117, 692397, 813797, 950505, 1103757, 1274837, 1465077, 1675857

Offset: 0

Author

Roger L. Bagula, Jan 20 2009

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A024003, A071237, A142463, A155120.

Programs

Magma

[2*n*(1+n+n^2+n^3)-3: n in [0..40] ]; // Vincenzo Librandi, May 23 2011

Maple

seq( -3 +2*n +2*n^2 +2*n^3 +2*n^4, n=0..40); # G. C. Greubel, Mar 25 2021

Mathematica

Table[-3 +2n +2n^2 +2n^3 +2n^4, {n, 0, 30}]

Sage

[-3 +2*n +2*n^2 +2*n^3 +2*n^4 for n in (0..40)] # G. C. Greubel, Mar 25 2021

Formula

a(n) = 2*n*(1 + n + n^2 + n^3) - 3.

G.f.: (3 - 20*x - 2*x^2 - 32*x^3 + 3*x^4)/(x-1)^5.

From Bruno Berselli, Dec 16 2010: (Start)

a(n) = 4*A071237(n) - 3.

a(n) = 2*A024003(n)/(1-n) - 5 (n>1). (End)

E.g.f.: (-3 + 8*x + 22*x^2 + 14*x^3 + 2*x^4)*exp(x). - G. C. Greubel, Mar 25 2021