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%I #10 Dec 30 2017 17:26:02
%S 1,1,2,11,30,91,303,936,2936,9300,29209,91917,289547,911218,2868341,
%T 9029949,28424456,89477119,281667368,886657081,2791106585,8786130132,
%U 27657838272,87064082194,274068969337,862741399379,2715822822365,8549136143060,26911817257385
%N Diagonal sums of the triangle A190152.
%H Nathaniel Johnston, <a href="/A190154/b190154.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k,3*n-6*k).
%F Conjecture: G.f. ( -1+x+x^3-x^4+2*x^2 ) / ( (x^3-3*x^2+4*x-1)*(x^3+3*x^2+2*x+1) ). - _R. J. Mathar_, Mar 15 2013
%p seq(add(binomial(3*n-4*k,3*n-6*k), k=0..floor(n/2)), n=0..20);
%t Table[Sum[Binomial[3n-4k,3n-6k],{k,0,n/2}],{n,0,28}]
%o (Maxima) makelist(sum(binomial(3*n-4*k,3*n-6*k),k,0,n/2),n,0,28);
%o (PARI) for(n=0,30, print1(sum(k=0,floor(n/2), binomial(3*n-4*k,3*n-6*k)), ", ")) \\ _G. C. Greubel_, Dec 30 2017
%Y Cf. A190152, A190153.
%K nonn,easy
%O 0,3
%A _Emanuele Munarini_, May 05 2011
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