A109438 a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).

1, 5, 18, 68, 253, 945, 3526, 13160, 49113, 183293, 684058, 2552940, 9527701, 35557865, 132703758, 495257168, 1848324913, 6898042485, 25743845026, 96077337620, 358565505453, 1338184684193, 4994173231318, 18638508241080

Offset: 0

Author

Creighton Dement, Jun 28 2005

Keywords

• easy
• nonn

Comments

See A109437 for comments.

Floretion Algebra Multiplication Program, FAMP Code: (-1)^(n)jbasejfor[ + .5'ii' + .5'kk' + .5'ij' + .5'ji' + .5'jk' + .5'kj'] 1vesfor = (-1,-1,-1,-1,)

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,3,-1).

Crossrefs

Cf. A109437, A001834, A102871.

Programs

Mathematica

LinearRecurrence[{3,3,-1},{1,5,18},30] (* Harvey P. Dale, Sep 07 2021 *)

PARI

Vec((1 + 2*x) / ((1 + x)*(1 - 4*x + x^2)) + O(x^30)) \\ Colin Barker, May 12 2019

Formula

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

a(n) = (-2*(-1)^n + (7-5*sqrt(3))*(2-sqrt(3))^n + (2+sqrt(3))^n*(7+5*sqrt(3))) / 12. - Colin Barker, May 12 2019