OFFSET
0,3
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 18 2003
STATUS
approved