

A110613


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


2



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
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OFFSET

0,3


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).


FORMULA

G.f.: (15*x+5*x^2)/((4*x1)*(2*x1)*(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).


MAPLE

seriestolist(series((15*x+5*x^2)/((4*x1)*(2*x1)*(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 *)


PROG

(PARI) x='x+O('x^50); Vec((15*x+5*x^2)/((4*x1)*(2*x1)*(x+1))) \\ G. C. Greubel, Sep 01 2017


CROSSREFS

Cf. A001045, A007582, A007581, A049775, A087440, A108618, A110614.
Sequence in context: A148767 A171180 A151358 * A337489 A088095 A333392
Adjacent sequences: A110610 A110611 A110612 * A110614 A110615 A110616


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Jul 31 2005


STATUS

approved



