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

Author

R. J. Mathar, Apr 24 2010

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A007896, A007897, A007898.

Programs

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

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 *)

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).