A172174 a(n) = 90*a(n-1) + 1.

1, 91, 8191, 737191, 66347191, 5971247191, 537412247191, 48367102247191, 4353039202247191, 391773528202247191, 35259617538202247191, 3173365578438202247191, 285602902059438202247191, 25704261185349438202247191, 2313383506681449438202247191

Offset: 1

Author

Mark Dols, Jan 28 2010

Keywords

• nonn
• easy

Comments

Difference of pairs of integers given in A162849.

Sum of digits give A017173.

Links

• Colin Barker, Table of n, a(n) for n = 1..512
• Index entries for linear recurrences with constant coefficients, signature (91,-90).

Crossrefs

Cf. A017173, A162849, A165154.

Programs

Mathematica

NestList[90#+1&,1,20] (* Harvey P. Dale, Aug 29 2014 *)

PARI

Vec(1/((x-1)*(90*x-1)) + O(x^30)) \\ Colin Barker, Oct 02 2015

SageMath

[(90^n -1)/89 for n in (1..50)] # G. C. Greubel, Apr 26 2022

Formula

From Colin Barker, Oct 02 2015: (Start)

a(n) = 91*a(n-1) - 90*a(n-2) for n>2.

G.f.: 1 / ((1-x)*(1-90*x)). (End)