A172162 a(n) = ( A165154(n) + A165155(n) )/2.

0, 1, 101, 10201, 1020401, 102050701, 10205121101, 1020513261601, 102051333512201, 10205133479922901, 1020513348977553701, 102051334912467474601, 10205133491373712765601, 1020513349139081705516701, 102051334913924160974827901, 10205133491392617410795809201

Offset: 0

Author

Mark Dols, Jan 27 2010

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (102,-101,-9900).

Crossrefs

Cf. A162741, A162849, A165154, A165155, A172163.

Programs

Mathematica

Table[99 100^n/9701 - 11^n/178 - (-9)^n/218, {n, 0, 20}] (* Bruno Berselli, Oct 02 2015 *)

PARI

concat(0, Vec(-x*(x-1)/((9*x+1)*(11*x-1)*(100*x-1)) + O(x^30))) \\ Colin Barker, Oct 02 2015

SageMath

[(-89*(-9)^n - 109*11^n + 198*10^(2*n))/19402 for n in (0..50)] # G. C. Greubel, Apr 24 2022

Formula

a(n) = 99*100^n/9701 - 11^n/178 - (-9)^n/218. [Bruno Berselli, Oct 02 2015]

From Colin Barker, Oct 02 2015: (Start)

a(n) = 102*a(n-1) - 101*a(n-2) - 9900*a(n-3) for n>3.

G.f.: x*(1-x) / ((1+9*x)*(1-11*x)*(1-100*x)).

(End)

Extensions

a(0) and more terms added by Bruno Berselli, Oct 02 2015