

A084136


Binomial transform of cosh(sqrt(2)*x)^2.


2



1, 1, 5, 13, 57, 201, 797, 2997, 11569, 44113, 169205, 647197, 2478825, 9488025, 36327821, 139071813, 532438369, 2038379425, 7803827429, 29876310829, 114379413657, 437893003113, 1676441901821, 6418134825429, 24571362963601
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OFFSET

0,3


COMMENTS

a(n) = (A084058(n) + 1)/2.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,5,7).


FORMULA

a(n) = ((1+sqrt(8))^n + (1sqrt(8))^n + 2)/4.
E.g.f.: exp(x)*cosh(sqrt(2)*x)^2.
G.f.: (1+x)*(3*x1) / ( (1x)*(7*x^2+2*x1) ).  R. J. Mathar, Nov 09 2012


MATHEMATICA

LinearRecurrence[{3, 5, 7}, {1, 1, 5}, 30] (* Harvey P. Dale, Nov 08 2017 *)


PROG

(PARI) x='x+O('x^30); round(Vec(serlaplace(exp(x)*cosh(sqrt(2)*x)^2))) \\ G. C. Greubel, Sep 11 2018
(MAGMA) I:=[1, 1, 5]; [n le 3 select I[n] else 3*Self(n1) +5*Self(n2)  7*Self(n3): n in [1..30]]; // G. C. Greubel, Sep 11 2018


CROSSREFS

Cf. A084137.
Sequence in context: A149550 A149551 A149552 * A091147 A149553 A149554
Adjacent sequences: A084133 A084134 A084135 * A084137 A084138 A084139


KEYWORD

easy,nonn


AUTHOR

Paul Barry, May 16 2003


STATUS

approved



