%I
%S 1,4,16,60,225,840,3136,11704,43681,163020,608400,2270580,8473921,
%T 31625104,118026496,440480880,1643897025,6135107220,22896531856,
%U 85451020204,318907548961,1190179175640,4441809153600,16577057438760,61866420601441,230888624967004
%N Expansion of 1/((1x^2)*(14*x+x^2)).
%H M. R. Bremner, <a href="http://arxiv.org/abs/1303.0920">Free associative algebras, noncommutative Grobner bases, and universal associative envelopes for nonassociative structures</a>, arXiv preprint arXiv:1303.0920, 2013
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,4,1).
%F a(n) = (1/12)*((74*sqrt(3))*(2sqrt(3))^n+(7+4*sqrt(3))*(2+sqrt(3))^n3+(1)^n). Recurrence: a(n) = 4*a(n1)4*a(n3)+a(n4).
%F a(n)=sum{k=0..floor(n/2), U(n2k, 2)}  _Paul Barry_, Nov 15 2003
%F The g.f. can also be written as 1/(14*x+4*x^3x^4), which relates this sequence to the family of sequences described in A225682.
%t CoefficientList[Series[1/((1x^2)*(14x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{4,0,4,1},{1,4,16,60},30] (* _Harvey P. Dale_, Aug 22 2015 *)
%o (PARI) Vec(1/((1x^2)*(14*x+x^2))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y EULER transform of A072279 (with its initial 1 omitted).
%Y A001353(n)^2 is a bisection of a(n).
%Y Cf. A225682.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 15 2002
