A014896 a(1) = 1, a(n) = 13*a(n-1) + n.

1, 15, 198, 2578, 33519, 435753, 5664796, 73642356, 957350637, 12445558291, 161792257794, 2103299351334, 27342891567355, 355457590375629, 4620948674883192, 60072332773481512, 780940326055259673, 10152224238718375767, 131978915103338884990, 1715725896343405504890

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 (15,-27,13).

Crossrefs

Row n=13 of A126885.

Programs

Magma

I:=[1, 15, 198]; [n le 3 select I[n] else 15*Self(n-1) - 27*Self(n-2)+ 13*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Maple

a:=n->sum((13^(n-j)-1)/12,j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 05 2007
a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,13]])^n)[2,3]:
seq(a(n), n=1..17);  # Alois P. Heinz, Aug 06 2008

Mathematica

LinearRecurrence[{15, -27, 13}, {1, 15, 198}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Maxima

a[1]:1$
a[2]:15$
a[3]:198$
a[n]:=15*a[n-1]-27*a[n-2]+13*a[n-3]$
A014896(n):=a[n]$ makelist(A014896(n),n,1,30); /* Martin Ettl, Nov 07 2012 */

Formula

a(n) = 15*a(n-1) - 27*a(n-2) + 13*a(n-3), with a(1)=1, a(2)=15, a(3)=198. - Vincenzo Librandi, Oct 20 2012

G.f.: x/((1-13*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020

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

E.g.f.: exp(x)*(13*exp(12*x) - 12*x - 13)/144.

a(n) = (13^(n+1) - 12*n - 11)/144. (End)