A110613 a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 0, a(2) = 3.

1, 0, 3, 7, 29, 107, 421, 1659, 6597, 26299, 105029, 419771, 1678405, 6712251, 26846277, 107379643, 429507653, 1718008763, 6871991365, 27487878075, 109951337541, 439805000635, 1759219303493, 7036875815867, 28147500467269

Offset: 0

Author

Creighton Dement, Jul 31 2005

Keywords

• easy
• nonn

Comments

A Jacobsthal related sequence (A001045). This sequence was calculated using the same rules given for A108618; the "initial seed" is the floretion given in the program code, below.

Links

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

Crossrefs

Cf. A001045, A007582, A007581, A049775, A087440, A108618, A110614.

Programs

Maple

seriestolist(series((1-5*x+5*x^2)/((4*x-1)*(2*x-1)*(x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2tessumseq[(.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(*) (from 3rd term, disregarding signs)

Mathematica

LinearRecurrence[{5, -2, -8}, {1, 0, 3}, 50] (* G. C. Greubel, Sep 01 2017 *)

PARI

x='x+O('x^50); Vec((1-5*x+5*x^2)/((4*x-1)*(2*x-1)*(x+1))) \\ G. C. Greubel, Sep 01 2017

Formula

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

Program "Superseeker" finds:

a(n) + a(n+1) = A007582(n) = A007581(n+1) - A007581(n).

a(n+2) - a(n) = A049775(n).

a(n) + 2*a(n+1) + a(n+2) = A087440(n+1).