A002447 Expansion of 1/(1-2*x^2-3*x^3).

1, 0, 2, 3, 4, 12, 17, 36, 70, 123, 248, 456, 865, 1656, 3098, 5907, 11164, 21108, 40049, 75708, 143422, 271563, 513968, 973392, 1842625, 3488688, 6605426, 12505251, 23676916, 44826780, 84869585, 160684308

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,3).

Programs

GAP

a:=[1,0,2];; for n in [4..40] do a[n]:=2*a[n-2]+3*a[n-3]; od; a; # G. C. Greubel, Jul 04 2019

Magma

I:=[1, 0, 2]; [n le 3 select I[n] else 2*Self(n-2)+3*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 11 2012

Mathematica

CoefficientList[Series[1/(1-2*x^2-3*x^3),{x,0,40}],x] (* Vincenzo Librandi, Jun 11 2012 *)
LinearRecurrence[{0,2,3}, {1,0,2}, 40] (* G. C. Greubel, Jul 04 2019 *)

PARI

Vec(1/(1-2*x^2-3*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

(1/(1-2*x-3*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 04 2019

Formula

From Paul Barry, Oct 16 2004: (Start)

a(n) = 2*a(n-2) + 3*a(n-3).

a(n) = Sum_{k=0..floor(n/2)} binomial(k, n-2*k)*2^k*(3/2)^(n-2*k). (End)