A116698 Expansion of -(1-x+3*x^2+x^3) / ((x^2+x-1)*(2*x^2+1)).

1, 0, 2, 5, 5, 4, 13, 29, 34, 39, 89, 176, 233, 313, 610, 1115, 1597, 2328, 4181, 7277, 10946, 16687, 28657, 48416, 75025, 117297, 196418, 326003, 514229, 815656, 1346269, 2211077, 3524578, 5637351, 9227465

Offset

0,3

Comments

a(2n) = F(2n+1) = A001519(n).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) for n > 3. - Colin Barker, May 18 2019

Mathematica

CoefficientList[Series[-(1-x+3x^2+x^3)/((x^2+x-1)(2x^2+1)), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, -1, 2, 2}, {1, 0, 2, 5}, 100] (* Harvey P. Dale, May 14 2022 *)

Prog

(PARI) Vec((1 - x + 3*x^2 + x^3) / ((1 - x - x^2)*(1 + 2*x^2)) + O(x^40)) \\ Colin Barker, May 18 2019

Crossrefs

Cf. A001519, A006498, A115008, A116697, A116699.

Sequence in context: A200484 A197004 A363764 * A246900 A277086 A229710

Adjacent sequences: A116695 A116696 A116697 * A116699 A116700 A116701

Keyword

easy,nonn

Author

Creighton Dement, Feb 23 2006

Status

approved