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
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).
Programs
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Magma
m:=30; R
:=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 -
Mathematica
LinearRecurrence[{3,1,-7,2,2},{1,0,4,6,20},30] (* Harvey P. Dale, May 05 2018 *) -
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
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
Comments