

A111643


Expansion of 2*(x+1)^2/((x^2+4*x+1)*(x^22*x1)).


7



2, 8, 34, 136, 530, 2032, 7714, 29104, 109378, 410040, 1534722, 5738360, 21441682, 80083808, 299027394, 1116348896, 4167148290, 15554127592, 58053908834, 216672484584, 808662529938, 3018041612880, 11263658377442, 42036964786320, 156885101002562
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OFFSET

0,1


COMMENTS

In reference to the program code, the sequence of Pell numbers A000126 is given by 1kbaseseq[C*J]. A001353 is 1ibaseiseq[C*J].


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,8,2,1).


FORMULA

From Colin Barker, May 01 2019: (Start)
a(n) = (3*(1sqrt(2))^(1+n)  3*(1+sqrt(2))^(1+n)  9*(2sqrt(3))^n  5*sqrt(3)*(2sqrt(3))^n  9*(2+sqrt(3))^n + 5*sqrt(3)*(2+sqrt(3))^n) / 6.
a(n) = 6*a(n1)  8*a(n2) + 2*a(n3) + a(n4) for n>3.
(End)


PROG

Floretion Algebra Multiplication Program, FAMP Code: 1baseiseq[C*J] with C =  'j + 'k  j' + k'  'ii'  'ij'  'ik'  'ji'  'ki' and J = + j' + k' + 1.5'ii' + .5'jj' + .5'kk' + .5e
(PARI) Vec(2*(1 + x)^2 / ((1 + 2*x  x^2)*(1 + 4*x + x^2)) + O(x^40)) \\ Colin Barker, May 01 2019


CROSSREFS

Cf. A111639, A111640, A111641, A111642, A111644, A000126.
Sequence in context: A026577 A204090 A226495 * A000163 A117616 A228655
Adjacent sequences: A111640 A111641 A111642 * A111644 A111645 A111646


KEYWORD

easy,sign


AUTHOR

Creighton Dement, Aug 10 2005


STATUS

approved



