A016133 Expansion of 1/((1-2*x)*(1-9*x)).
1, 11, 103, 935, 8431, 75911, 683263, 6149495, 55345711, 498111911, 4483008223, 40347076055, 363123688591, 3268113205511, 29413018865983, 264717169826615, 2382454528505071, 21442090756676711, 192978816810352543, 1736809351293697175, 15631284161644323151
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Kalika Prasad, Munesh Kumari, Rabiranjan Mohanta, and Hrishikesh Mahato, The sequence of higher order Mersenne numbers and associated binomial transforms, arXiv:2307.08073 [math.NT], 2023.
- Index entries for linear recurrences with constant coefficients, signature (11,-18).
Programs
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Magma
[+9^(n+1)/7 -2^(n+1)/7 : n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
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Mathematica
CoefficientList[Series[1/((1-2x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[ {11,-18},{1,11},30] (* Harvey P. Dale, Apr 19 2020 *) -
PARI
Vec(1/((1-2*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
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Sage
[lucas_number1(n,11,18) for n in range(1, 20)] # Zerinvary Lajos, Apr 27 2009
Formula
a(n) = 11*a(n-1) - 18*a(n-2).
a(n) = a(n) = 9*a(n-1) + 2^n. - Paul Curtz, Feb 14 2008
E.g.f.: exp(2*x)*(9*exp(7*x) - 2)/7. - Stefano Spezia, Jul 30 2022