A172163 a(n) = ( A165155(n) - A165154(n) )/2.

0, 0, 10, 1020, 103030, 10307040, 1030814050, 103082025060, 10308214641070, 1030821549763080, 103082156348992090, 10308215646124529100, 1030821564770799275110, 103082156478507926931120, 10308215647869324982098130, 1030821564787110934730377140

Offset: 0

Author

Mark Dols, Jan 27 2010

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..501
• Index entries for linear recurrences with constant coefficients, signature (102,-101,-9900).

Crossrefs

Cf. A162741, A162849, A165154, A165155, A172162.

Programs

Mathematica

Table[10^(2 n + 1)/9701 - 11^n/178 + (-9)^n/218, {n, 0, 20}] (* Bruno Berselli, Oct 02 2015 *)
LinearRecurrence[{102,-101,-9900},{0,0,10},20] (* Harvey P. Dale, Aug 17 2021 *)

PARI

concat([0,0], Vec(10*x^2/((9*x+1)*(11*x-1)*(100*x-1)) + O(x^30))) \\ Colin Barker, Oct 02 2015

SageMath

[(89*(-9)^n + 2*10^(2*n+1) - 109*11^n)/19402 for n in (0..50)] # G. C. Greubel, Apr 24 2022

Formula

a(n) = 10^(2*n+1)/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>2.

G.f.: 10*x^2 / ((1+9*x)*(1-11*x)*(1-100*x)).

(End)

Extensions

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