A171753 - OEIS

%I #23 May 11 2024 17:14:06

%S 1,3,10,36,137,543,2218,9264,39329,168939,731770,3188364,13948745,

%T 61196775,269007994,1184076216,5216618369,22996827795,101421591466,

%U 447422614068,1974197123657,8712062181999,38449506441994,169702143024768,749034931995041,3306200447618043

%N Expansion of g.f. 1/(1-3*x-x^2/(1-3*x-x^2/(1-3*x))).

%C 3rd binomial transform of 1,0,1,0,2,0,4,0,8,0,...

%H Stefano Spezia, <a href="/A171753/b171753.txt">Table of n, a(n) for n = 0..1500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-25,21).

%F G.f.: (1-6x+8x^2)/(1-9x+25x^2-21x^3) = -(4*x-1)*(2*x-1)/((3*x-1)*(7*x^2-6*x+1)).

%F a(n) = (3-sqrt(2))^n/4 + (3+sqrt(2))^n/4 + 3^n/2.

%F a(n) = (3^n+A083878(n))/2. - _R. J. Mathar_, Oct 08 2016

%F E.g.f.: exp(3*x)*cosh(x/sqrt(2))^2. - _Stefano Spezia_, May 11 2024

%t LinearRecurrence[{9,-25,21},{1,3,10},26] (* _Stefano Spezia_, May 11 2024 *)

%Y Cf. A083878.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Dec 17 2009