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%I #14 Jan 15 2016 02:44:48
%S 1,2,2,2,5,2,2,6,6,2,2,6,9,6,2,2,6,10,10,6,2,2,6,10,13,10,6,2,2,6,10,
%T 14,14,10,6,2,2,6,10,14,17,14,10,6,2,2,6,10,14,18,18,14,10,6,2,2,6,10,
%U 14,18,21,18,14,10,6,2
%N Correlation triangle for the sequence 2-0^n.
%C Row sums are (n+1)^2 (A000290(n+1)). Diagonal sums are the Molien series A007980. T(2n,n) is 4n+1 (A016813), the partial sums of (2-0^n)^2. T(2,n)-T(2n,n+1) is 3-2*0^n.
%C From _Mats Granvik_, Jul 06 2010: (Start)
%C If seen as a square array:
%C 1, 2, 2, 2
%C 2, 5, 6, 6
%C 2, 6, 9, 10
%C 2, 6, 10, 13
%C then the matrix inverse contains the same values, only signed and in reversed order:
%C 13, -10, 6, -2
%C -10, 9, -6, 2
%C 6, -6, 5, -2
%C -2, 2, -2, 1
%C (End)
%F G.f.: (1+x)(1+x*y)/((1-x)(1-x*y)(1-x^2*y)).
%F T(n, k) = sum{j=0..n, [j<=k]*(2-0^(k-j))*[j<=n-k]*(2-0^(n-k-j))}.
%e Triangle begins
%e 1;
%e 2,2;
%e 2,5,2;
%e 2,6,6,2;
%e 2,6,9,6,2;
%e 2,6,10,10,6,2;
%t Flatten[Table[Table[If[n - k + 1 == k, 4*(n - k + 1 - 1) + 1, If[n - k + 1 > k, 4*(k - 1) + 2, 4*(n - k + 1 - 1) + 2]], {k, 1, n}], {n, 1, 11}]] (* _Mats Granvik_, Jan 06 2016 *)
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Jan 19 2006
%E a(65)-a(66) from _Mats Granvik_, Jan 06 2016
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