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%I #14 Jun 13 2015 00:51:20
%S 1,3,4,12,13,39,40,120,121,363,364,1092,1093,3279,3280,9840,9841,
%T 29523,29524,88572,88573,265719,265720,797160,797161,2391483,2391484,
%U 7174452,7174453,21523359,21523360,64570080,64570081,193710243,193710244
%N Expansion of (1+3x)/((1-x^2)(1-3x^2)).
%C Add 1, triple, add 1, triple, ... (of course this is simply a restatement of one of _Philippe Deléham_'s formulas). - _Jon Perry_, Aug 11 2014
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-3).
%F a(n)=4a(n-2)-3a(n-4); a(n)=3*3^(n/2)(1/4+sqrt(3)/4+(1/4-sqrt(3)/4)(-1)^n)+(-1)^n/2-1.
%F a(n) = a(n-1)*3 if n odd; a(n) = a(n-1)+1 if n even. - _Philippe Deléham_, Apr 22 2013
%F a(2n) = A003462(n+1); a(2n+1) = A123109(n+1) = A029858(n+1). - _Philippe Deléham_, Apr 22 2013
%Y Cf. A075427, A080610, A083416.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 22 2004
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