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A088014 Expansion of e.g.f.: cosh(sqrt(2)*x)*(1+exp(x)). 3
2, 1, 5, 7, 21, 41, 107, 239, 593, 1393, 3395, 8119, 19665, 47321, 114371, 275807, 666113, 1607521, 3881411, 9369319, 22620561, 54608393, 131838371, 318281039, 768402497, 1855077841, 4478562275, 10812186007, 26102942481, 63018038201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-2)

FORMULA

G.f.: (x-2)*(2*x-1)*(1+x) / ( (2*x^2-1)*(x^2+2*x-1) ).

E.g.f.: cosh(sqrt(2)*x)*(1+exp(x)).

a(n) = ((sqrt(2))^n + (-sqrt(2))^n + (1+sqrt(2))^n + (1-sqrt(2))^n)/2.

a(0)=2, a(1)=1, a(2)=5, a(3)=7, a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 2*a(n-4). - Harvey P. Dale, Jul 31 2012

MATHEMATICA

With[{nn=30}, CoefficientList[Series[Cosh[Sqrt[2]x](1+Exp[x]), {x, 0, nn}], x]Range[0, nn]!] (* or *) LinearRecurrence[{2, 3, -4, -2}, {2, 1, 5, 7}, 30] (* Harvey P. Dale, Jul 31 2012 *)

PROG

(PARI) x='x+O('x^50); Vec((x-2)*(2*x-1)*(1+x)/((2*x^2-1)*(x^2+2*x-1))) \\ G. C. Greubel, Aug 16 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x-2)*(2*x-1)*(1+x)/((2*x^2-1)*(x^2+2*x-1)))); // G. C. Greubel, Aug 16 2018

CROSSREFS

Cf. A052950.

Cf. A002315.

Sequence in context: A005297 A014551 A175002 * A193662 A279508 A175770

Adjacent sequences:  A088011 A088012 A088013 * A088015 A088016 A088017

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 18 2003

STATUS

approved

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Last modified April 22 10:22 EDT 2019. Contains 322330 sequences. (Running on oeis4.)