A188475 a(n) = (2*n^3 + 3*n^2 + n + 3)/3.

1, 3, 11, 29, 61, 111, 183, 281, 409, 571, 771, 1013, 1301, 1639, 2031, 2481, 2993, 3571, 4219, 4941, 5741, 6623, 7591, 8649, 9801, 11051, 12403, 13861, 15429, 17111, 18911, 20833, 22881, 25059, 27371, 29821, 32413, 35151, 38039, 41081, 44281, 47643

Offset: 0

Author

Paul Barry, Apr 01 2011

Keywords

• nonn
• easy

Comments

Hankel transform of A137398(n+1) (conjecture).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[(2*n^3+3*n^2+n+3)/3: n in [0..50]]; // Vincenzo Librandi, Nov 25 2011

Maple

A188475:=n->(2*n^3+3*n^2+n+3)/3; seq(A188475(n),n=0..100); # Wesley Ivan Hurt, Nov 11 2013

Mathematica

LinearRecurrence[{4,-6,4,-1},{1,3,11,29},100] (* Vincenzo Librandi, Nov 25 2011 *)

Formula

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

a(n) = A006331(n) + 1. - Bruno Berselli, Nov 14 2011