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

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (14,-25,12).

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A341500 A254811 A099158 * A048443 A191690 A016136

Adjacent sequences: A014879 A014880 A014881 * A014883 A014884 A014885

Keyword

nonn

Author

N. J. A. Sloane, Olivier Gérard

Status

approved