

A077921


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


3



1, 1, 4, 8, 21, 49, 120, 288, 697, 1681, 4060, 9800, 23661, 57121, 137904, 332928, 803761, 1940449, 4684660, 11309768, 27304197, 65918161, 159140520, 384199200, 927538921, 2239277041, 5406093004, 13051463048, 31509019101, 76069501249, 183648021600
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OFFSET

0,3


COMMENTS

Partial sums of sequence of signed Pell numbers (1)^n*A000129(n).  Paul Barry, May 09 2003


LINKS

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


FORMULA

G.f.: 1/((1x)*(1+2*xx^2)).
From Colin Barker, Apr 15 2016: (Start)
a(n) = a(n1)+3*a(n2)a(n3) for n>2.
a(n) = (2(1sqrt(2))^(1+n)(1+sqrt(2))^(1+n))/4.
(End)
E.g.f.: (1/4)*(2*exp(x) + (1 + sqrt(2))*exp((1sqrt(2))*x)  (sqrt(2)  1)*exp((sqrt(2)1)*x)).  Ilya Gutkovskiy, Apr 15 2016


MATHEMATICA

CoefficientList[Series[(1/(1x))/(1+2xx^2), {x, 0, 50}], x] (* Harvey P. Dale, Mar 20 2011 *)


PROG

(PARI) Vec((1x)^(1)/(1+2*xx^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012


CROSSREFS

a(3n) = A048739(n).
Sequence in context: A180608 A244583 A261031 * A097076 A003608 A248423
Adjacent sequences: A077918 A077919 A077920 * A077922 A077923 A077924


KEYWORD

sign,easy


AUTHOR

N. J. A. Sloane, Nov 17 2002


STATUS

approved



