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%I #10 Jul 15 2017 11:07:39
%S 1,1,1,1,2,1,2,2,2,2,2,3,3,3,2,2,4,4,4,4,2,3,4,5,7,5,4,3,3,5,6,8,8,6,
%T 5,3,3,6,7,9,11,9,7,6,3,4,6,8,12,12,12,12,8,6,4,4,7,9,13,15,15,15,13,
%U 9,7,4
%N Correlation triangle for floor((n+3)/3).
%C Row sums are A115266. Diagonal sums are A115267.
%C T(2n,n) is A092353. T(2n,n)-T(2n,n+1)=A087508(n+1).
%F G.f.: (1+x+x^2)(1+xy+x^2*y^2)/((1-x^3)^2*(1-x^3*y^3)^2*(1-x^2*y)).
%F T(n, k) = sum{j=0..n, [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3)}.
%e Triangle begins
%e 1;
%e 1,1;
%e 1,2,1;
%e 2,2,2,2;
%e 2,3,3,3,2;
%e 2,4,4,4,4,2;
%e 3,4,5,7,5,4,3;
%e 3,5,6,8,8,6,5,3;
%e 3,6,7,9,11,9,7,6,3;
%t T[n_, k_] := Sum[Boole[j <= k] * Floor[(k - j + 3)/3] * Boole[j <= n-k] * Floor[(n - k - j + 3)/3], {j, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 15 2017 *)
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Jan 18 2006
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