A107475 a(n)= 5*a(n-1) +3*a(n-2) -15*a(n-3) +5*a(n-4) +3*a(n-5) -a(n-6).

1, 1, 2, 3, 5, 12, 42, 191, 933, 4680, 23575, 118989, 600666, 3032680, 15311545, 77306765, 390314982, 1970668439, 9949740765, 50235420192, 253634480330, 1280579531127, 6465540187905, 32643977982772, 164816746432131

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (5, 3, -15, 5, 3, -1).

Formula

G.f.: (1-4*x-6*x^2+5*x^3-6*x^4)/( (x^3-5*x^2+6*x-1)*(x^3+2*x^2-x-1) ).

Mathematica

m=3 M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, m, (m + 2), -m*(m + 2), m, (m + 2)}} v[0] = {0, 1, 1, 2, 3, 5} v[n_] := M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{5, 3, -15, 5, 3, -1}, {1, 1, 2, 3, 5, 12}, 30] (* Harvey P. Dale, Aug 30 2021 *)

Crossrefs

Sequence in context: A000997 A266541 A301929 * A108225 A259503 A193064

Adjacent sequences: A107472 A107473 A107474 * A107476 A107477 A107478

Keyword

nonn,easy

Author

Roger L. Bagula, May 27 2005

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

Status

approved