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%I #9 Dec 12 2013 19:03:42
%S 1,1,-1,-2,0,0,-3,1,8,1,1,26,7,-51,-3,0,-264,-186,348,-120,-285,2697,
%T 2871,-2304,3393,8029,-25795,-36872,16108,-60010,-159683,213795,
%U 413712,-181857,833779,2669534,-1272977,-4030235,3611168,-9145271,-39467427
%N A generalized Chebyshev transform of the Motzkin numbers A001006.
%C Hankel transform is the (1,3) Somos-4 sequence A174170.
%F G.f.: (1-x+3x^2-sqrt(1-2x+3x^2-6x^3+9x^4))/(2x^2)=(1/(1+3x))*M(x/(1+3x^2)), M(x) the g.f. of A010006;
%F a(n) = sum{k=0..floor(n/2), (-3)^k*A001006(n-2k)}.
%F Conjecture: (n+2)*a(n) -(2*n+1)*a(n-1) +3*(n-1)*a(n-2) +3*(5-2*n)*a(n-3) +9*(n-4)*a(n-4)=0. - _R. J. Mathar_, Sep 30 2012
%K easy,sign
%O 0,4
%A _Paul Barry_, Mar 10 2010
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