OFFSET
0,2
COMMENTS
Binomial transform of A048495. Second binomial transform of 1, 1, 3, 5, 7, ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-21,18).
FORMULA
G.f.: (1 - 5*x + 8*x^2)/((1-2*x)*(1-3*x)^2). - Colin Barker, Mar 22 2012
E.g.f.: 2*exp(2*x) + (2*x-1)*exp(3*x). - G. C. Greubel, Mar 22 2023
MATHEMATICA
LinearRecurrence[{8, -21, 18}, {1, 3, 11}, 30] (* Harvey P. Dale, Dec 12 2015 *)
PROG
(Magma) [3^(n-1)*(2*n-3)+2^(n+1) : n in [0..30]]; // Vincenzo Librandi, Sep 25 2011
(PARI) Vec((1-5*x+8*x^2)/(1-2*x)/(1-3*x)^2+O(x^99)) \\ Charles R Greathouse IV, Mar 22 2012
(SageMath) [2^(n+1) +3^(n-1)*(2*n-3) for n in range(41)] # G. C. Greubel, Mar 22 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jun 09 2003
STATUS
approved