

A102129


Expansion of (1  x)*(1 + 2*x) / ((1 + x)*(1  4*x  x^2)).


1



1, 4, 15, 66, 277, 1176, 4979, 21094, 89353, 378508, 1603383, 6792042, 28771549, 121878240, 516284507, 2187016270, 9264349585, 39244414612, 166242008031, 704212446738, 2983091794981, 12636579626664, 53529410301635, 226754220833206, 960546293634457
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OFFSET

0,2


COMMENTS

A floretiongenerated, Pellian related sequence.
Sequence results from a force transform of the periodic sequence with initial period (1, 1).


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5,1).


FORMULA

a(n) + a(n+1) = A048875(n+1)  A048875(n).
a(n) = (10*(1)^n + (2sqrt(5))^n*(15+sqrt(5))  (2+sqrt(5))^n*(15+sqrt(5))) / 20.  Colin Barker, Jun 06 2017


MATHEMATICA

CoefficientList[ Series[((1 + x)(2x + 1))/((1 + x)(x^2 + 4x  1)), {x, 0, 22}], x] (* Robert G. Wilson v, Mar 16 2005 *)


PROG

Floretion Algebra Multiplication Program, FAMP Code: 2ibaseiforseq[A*B] with A =  .5'j + .5'k  .5j' + .5k'  'ii'  .5'ij'  .5'ik'  .5'ji'  .5'ki' B =  .5'ii' + .5'jj' + .5'kk' + .5e, 1vesforseq(n) = (1)^n, 2basekforseq[A*B] = A048875, ForType: 1A
(PARI) Vec((1  x)*(1 + 2*x) / ((1 + x)*(1  4*x  x^2)) + O(x^30)) \\ Colin Barker, Jun 06 2017


CROSSREFS

Cf. A048875.
Sequence in context: A233536 A318121 A097422 * A164310 A011967 A250886
Adjacent sequences: A102126 A102127 A102128 * A102130 A102131 A102132


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Mar 15 2005


EXTENSIONS

Corrected and extended by Robert G. Wilson v, Mar 16 2005


STATUS

approved



