OFFSET
0,2
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).
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved