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%I #5 Nov 16 2012 04:10:11
%S 1,1,2,3,5,8,14,24,43,78,144,269,509,971,1868,3618,7049,13805,27162,
%T 53661,106405,211697,422458,845386,1696017,3410522,6873060,13878721,
%U 28077439,56900936,115501012,234807488,478032437,974507543,1989123814
%N Diagonal sums of the number triangle associated to A086617.
%C The triangle associated to A086617 is given by T(n,k)=if(k<=n, sum{j=0..n-k, C(n-k,j)C(k,j)C(j)},0). A050253(n)=A108296(n+2)-A108296(n).
%F G.f.: (1-x^2-sqrt(1-2x^2-4x^3-3x^4))/(2*x^3(1-x^2)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k, C(n-2k, j)C(k, j)C(j)}.
%F Conjecture: (n+3)*a(n) +(-n-2)*a(n-1) +2*(-n-1)*a(n-2) +2*(-n+3)*a(n-3) +(n+1)*a(n-4) +3*(n-2)*a(n-5)=0. - _R. J. Mathar_, Nov 16 2012
%K easy,nonn
%O 0,3
%A _Paul Barry_, May 31 2005
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