A088015 Expansion of e.g.f. cosh(sqrt(2)*x) + exp(x)*(cosh(sqrt(2)*x) - 1).

1, 0, 4, 6, 20, 40, 106, 238, 592, 1392, 3394, 8118, 19664, 47320, 114370, 275806, 666112, 1607520, 3881410, 9369318, 22620560, 54608392, 131838370, 318281038, 768402496, 1855077840, 4478562274, 10812186006, 26102942480, 63018038200

Offset

0,3

Comments

This sequence is A000079 (with interpolated zeros) + 2*(A048739 (with two leading zeros)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..2600

Index entries for linear recurrences with constant coefficients, signature (3,1,-7,2,2).

Formula

a(n) = A088014(n)-1.

G.f.: (1 -3*x +3*x^2 +x^3 -4*x^4)/((1-x)*(1-2*x-3*x^2+4*x^3+2*x^4)).

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

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

G.f.: ( -1-3*x^2-x^3+4*x^4+3*x ) / ( (x-1)*(2*x^2-1)*(x^2+2*x-1) ). - R. J. Mathar, Dec 10 2014

Mathematica

LinearRecurrence[{3, 1, -7, 2, 2}, {1, 0, 4, 6, 20}, 30] (* Harvey P. Dale, May 05 2018 *)

Prog

(PARI) x='x+O('x^30); Vec((1 -3*x +3*x^2 +x^3 -4*x^4)/((1-x)*(1-2*x-3*x^2+4*x^3+2*x^4))) \\ G. C. Greubel, Sep 27 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 -3*x +3*x^2 +x^3 -4*x^4)/((1-x)*(1-2*x-3*x^2+4*x^3+2*x^4)))); // G. C. Greubel, Sep 27 2018

Crossrefs

Sequence in context: A026788 A079435 A227959 * A027377 A048789 A038069

Adjacent sequences: A088012 A088013 A088014 * A088016 A088017 A088018

Keyword

easy,nonn

Author

Paul Barry, Sep 18 2003

Status

approved