A014881 a(1)=1, a(n) = 11*a(n-1) + n.

1, 13, 146, 1610, 17715, 194871, 2143588, 23579476, 259374245, 2853116705, 31384283766, 345227121438, 3797498335831, 41772481694155, 459497298635720, 5054470284992936, 55599173134922313, 611590904484145461, 6727499949325600090, 74002499442581601010

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 (13,-23,11).

Crossrefs

Row n=11 of A126885.

Programs

Magma

I:=[1, 13, 146]; [n le 3 select I[n] else 13*Self(n-1) - 23*Self(n-2)+ 11*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Maple

a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,11]])^n)[2,3]:
seq(a(n), n=1..17);  # Alois P. Heinz, Aug 06 2008

Mathematica

LinearRecurrence[{13, -23, 11}, {1, 13, 146}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Formula

a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3), with a(1)=1, a(2)=13, a(3)=146. - Vincenzo Librandi, Oct 20 2012

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

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

E.g.f.: exp(x)*(11*exp(10*x) - 10*x - 11)/100.

a(n) = (11^(n+1) - 10*n - 11)/100. (End)