A172175 a(n) = 110*a(n-1) + 1.

1, 111, 12211, 1343211, 147753211, 16252853211, 1787813853211, 196659523853211, 21632547623853211, 2379580238623853211, 261753826248623853211, 28792920887348623853211, 3167221297608348623853211, 348394342736918348623853211, 38323377701061018348623853211

Offset: 1

Author

Mark Dols, Jan 28 2010

Keywords

• nonn
• easy

Comments

Sum of pairs of integers given in A162849. Sum of digits give A000225.

Links

• Colin Barker, Table of n, a(n) for n = 1..490
• Index entries for linear recurrences with constant coefficients, signature (111,-110).

Crossrefs

Cf. A000225, A162849, A165155.

Programs

Mathematica

a = {1}; Do[AppendTo[a, 110 a[[n-1]] + 1], {n, 2, 15}]; a (* Michael De Vlieger, Oct 02 2015 *)

PARI

Vec(1/((x-1)*(110*x-1)) + O(x^30)) \\ Colin Barker, Oct 02 2015

SageMath

[((110)^n -1)/109 for n in (1..50)] # G. C. Greubel, Apr 26 2022

Formula

From Colin Barker, Oct 02 2015: (Start)

a(n) = 111*a(n-1) - 110*a(n-2) for n>2.

G.f.: 1 / ((1-x)*(1-110*x)). (End)