A014882 a(1) = 1, a(n) = 12*a(n-1) + n.

1, 14, 171, 2056, 24677, 296130, 3553567, 42642812, 511713753, 6140565046, 73686780563, 884241366768, 10610896401229, 127330756814762, 1527969081777159, 18335628981325924, 220027547775911105, 2640330573310933278, 31683966879731199355, 380207602556774392280

Offset: 1

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (14,-25,12).

Crossrefs

Row n=12 of A126885.

Programs

Magma

I:=[1, 14, 171]; [n le 3 select I[n] else 14*Self(n-1) - 25*Self(n-2)+ 12*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Maple

a:=n->sum((12^(n-j)-1^(n-j))/11,j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 12 2007
a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,12]])^n)[2,3]:
seq(a(n), n=1..17);  # Alois P. Heinz, Aug 06 2008

Mathematica

LinearRecurrence[{14, -25, 12}, {1, 14, 171}, 201] (* Vincenzo Librandi, Oct 20 2012 *)

Formula

a(n) = 14*a(n-1) - 25*a(n-2) + 12*a(n-3), with a(1)=1, a(2)=14, a(3)=171. - Vincenzo Librandi, Oct 20 2012

G.f.: x/((1-12*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020

From Elmo R. Oliveira, Mar 31 2025: (Start)

E.g.f.: exp(x)*(12*exp(11*x) - 11*x - 12)/121.

a(n) = (12^(n+1) - 11*n - 12)/121. (End)