A084136 Binomial transform of cosh(sqrt(2)*x)^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

Offset

0,3

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 + (1-sqrt(8))^n + 2)/4.

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

E.g.f.: exp(x)*cosh(sqrt(2)*x)^2.

G.f.: (1+x)*(1-3*x) / ( (1-x)*(1-2*x-7*x^2) ). - R. J. Mathar, Nov 09 2012

Mathematica

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

Prog

(PARI) my(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(n-1) +5*Self(n-2) - 7*Self(n-3): n in [1..30]]; // G. C. Greubel, Sep 11 2018
(SageMath)
A084058=BinaryRecurrenceSequence(2, 7, 1, 1)
def A084136(n): return (1+A084058(n))/2
[A084136(n) for n in range(41)] # G. C. Greubel, Oct 13 2022

Crossrefs

Cf. A084058, A084137.

Sequence in context: A149550 A149551 A149552 * A091147 A351072 A149553

Adjacent sequences: A084133 A084134 A084135 * A084137 A084138 A084139

Keyword

easy,nonn

Author

Paul Barry, May 16 2003

Status

approved