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%I #15 Dec 31 2023 16:56:36
%S 1,0,4,6,20,40,106,238,592,1392,3394,8118,19664,47320,114370,275806,
%T 666112,1607520,3881410,9369318,22620560,54608392,131838370,318281038,
%U 768402496,1855077840,4478562274,10812186006,26102942480,63018038200
%N Expansion of e.g.f. cosh(sqrt(2)*x) + exp(x)*(cosh(sqrt(2)*x) - 1).
%C This sequence is A000079 (with interpolated zeros) + 2*(A048739 (with two leading zeros)).
%H G. C. Greubel, <a href="/A088015/b088015.txt">Table of n, a(n) for n = 0..2600</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-7,2,2).
%F a(n) = A088014(n)-1.
%F 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)).
%F E.g.f. : cosh(sqrt(2)x)+exp(x)(cosh(sqrt(2)x)-1);
%F a(n) = ((sqrt(2))^n +(-sqrt(2))^n +(1+sqrt(2))^n +(1-sqrt(2))^n)/2 -1.
%F 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
%t LinearRecurrence[{3,1,-7,2,2},{1,0,4,6,20},30] (* _Harvey P. Dale_, May 05 2018 *)
%o (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
%o (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
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 18 2003
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