A175378 G.f. x^4*(2*x^2-1)/( (x^2-1)*(x^2+x-1)*(2*x^3-2*x^2+2*x-1) ).

0, 0, 0, 0, 1, 3, 5, 8, 14, 26, 45, 75, 125, 212, 358, 598, 993, 1651, 2745, 4552, 7526, 12426, 20501, 33787, 55605, 91404, 150118, 246350, 403929, 661763, 1083393, 1772512, 2898182, 4735938, 7734765, 12626059, 20600733, 33597188, 54769606

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

F. V. Weinstein, Notes on Fibonacci Partitions, arXiv:math/0307150, variable h(n).

Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 3, -4, 0, 2).

Formula

a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-7).

Mathematica

LinearRecurrence[{3, -2, -1, 3, -4, 0, 2}, {0, 0, 0, 0, 1, 3, 5}, 40] (* Harvey P. Dale, Mar 07 2012 *)
CoefficientList[Series[x^4*(2*x^2 - 1)/((x^2 - 1)*(x^2 + x - 1)*(2*x^3 - 2*x^2 + 2*x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 20 2012 *)

Prog

(Magma) I:=[0, 0, 0, 0, 1, 3, 5]; [n le 7 select I[n] else 3*Self(n-1) - 2*Self(n-2) - Self(n-3) + 3*Self(n-4) - 4*Self(n-5) + 2*Self(n-7): n in [1..40]]; // Vincenzo Librandi, Dec 20 2012

Crossrefs

Cf. A007896, A007897, A007898.

Sequence in context: A329823 A329742 A078065 * A072655 A108301 A282390

Adjacent sequences: A175375 A175376 A175377 * A175379 A175380 A175381

Keyword

nonn,easy

Author

R. J. Mathar, Apr 24 2010

Status

approved