A110614 a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.

1, 5, 15, 57, 215, 841, 3319, 13193, 52599, 210057, 839543, 3356809, 13424503, 53692553, 214759287, 859015305, 3436017527, 13743982729, 54975756151, 219902675081, 879610001271, 3518438606985, 14073751631735, 56295000934537, 225179992553335, 900719947843721

Offset: 0

Author

Creighton Dement, Jul 31 2005

Keywords

• easy
• nonn

Comments

See comment for A110613.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-2,-8).

Crossrefs

Cf. A110613, A063376.

Programs

Maple

seriestolist(series((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2ibasejsumseq[(.5'i - .5'k - .5i' + .5k' - .5'ij' - .5'ji' - .5'jk' - .5'kj')('i + j' + 'ij' + 'ji')] Sumtype is set to: sum[Y[15]] = sum[ * ] (disregarding signs)

Mathematica

LinearRecurrence[{5,-2,-8},{1,5,15},30] (* Harvey P. Dale, Dec 28 2013 *)

PARI

Vec((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)) + O(x^30)) \\ Colin Barker, Feb 05 2017

Formula

G.f.: (1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)).

a(n) + a(n+1) = A063376(n+1).

a(n) = (-7*(-1)^n + 5*2^(1+n) + 3*4^(1+n)) / 15. - Colin Barker, Feb 05 2017