A121509 a(n) = 5*n^2/2 - 5*n + 13/4 - (-1)^n/4.

1, 3, 11, 23, 41, 63, 91, 123, 161, 203, 251, 303, 361, 423, 491, 563, 641, 723, 811, 903, 1001, 1103, 1211, 1323, 1441, 1563, 1691, 1823, 1961, 2103, 2251, 2403, 2561, 2723, 2891, 3063, 3241, 3423, 3611, 3803, 4001, 4203, 4411, 4623, 4841, 5063, 5291, 5523

Offset: 1

Author

Roger L. Bagula, Sep 07 2006

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A001849, A003215, A005448.

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{1,3,11,23},50] (* Harvey P. Dale, Oct 17 2020 *)

PARI

a(n) = 5*n^2/2 - 5*n + 13/4 - (-1)^n/4; \\ Jinyuan Wang, Jun 07 2020

PARI

Vec(x*(1 + x + 5*x^2 + 3*x^3) / ((1 - x)^3*(1 + x)) + O(x^40)) \\ Colin Barker, Jun 08 2020

Formula

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

a(n) = 1 + 2*(n-1)^2 + floor((n-1)^2/2). - Wesley Ivan Hurt, Jun 14 2013

G.f.: x*(1 + x + 5*x^2 + 3*x^3) / ((1 - x)^3*(1 + x)). - Colin Barker, Jun 08 2020

Extensions

Definition replaced by polynomial - The Assoc. Editors of the OEIS, Oct 14 2009