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A172162
a(n) = ( A165154(n) + A165155(n) )/2.
3
0, 1, 101, 10201, 1020401, 102050701, 10205121101, 1020513261601, 102051333512201, 10205133479922901, 1020513348977553701, 102051334912467474601, 10205133491373712765601, 1020513349139081705516701, 102051334913924160974827901, 10205133491392617410795809201
OFFSET
0,3
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)
MATHEMATICA
Table[99 100^n/9701 - 11^n/178 - (-9)^n/218, {n, 0, 20}] (* Bruno Berselli, Oct 02 2015 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, Jan 27 2010
EXTENSIONS
a(0) and more terms added by Bruno Berselli, Oct 02 2015
STATUS
approved