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

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-23,11).

Formula

a(n) = -11/100 + 11/100*11^n - 1/10*n, with n>=1. - Paolo P. Lava, Jan 14 2009

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

Maple

a:=n->sum(11^(n-j)*j, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jun 05 2008
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 *)

Prog

(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

Crossrefs

Sequence in context: A297223 A199023 A152585 * A048442 A353107 A051524

Adjacent sequences: A014878 A014879 A014880 * A014882 A014883 A014884

Keyword

nonn

Author

N. J. A. Sloane, Olivier Gérard

Status

approved