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A016133
Expansion of 1/((1-2*x)*(1-9*x)).
9
1, 11, 103, 935, 8431, 75911, 683263, 6149495, 55345711, 498111911, 4483008223, 40347076055, 363123688591, 3268113205511, 29413018865983, 264717169826615, 2382454528505071, 21442090756676711, 192978816810352543, 1736809351293697175, 15631284161644323151
OFFSET
0,2
LINKS
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.
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
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 *)
PROG
(Sage) [lucas_number1(n, 11, 18) for n in range(1, 20)] # Zerinvary Lajos, Apr 27 2009
(Magma) [+9^(n+1)/7 -2^(n+1)/7 : n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
(PARI) Vec(1/((1-2*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012
CROSSREFS
Cf. A016204 (partial sums); A191465 (this sequence times 7).
Sequence in context: A156948 A287302 A141915 * A287833 A155594 A077250
KEYWORD
nonn,easy
STATUS
approved