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%I #3 Mar 30 2012 18:59:13
%S 1,3,3,4,10,4,4,15,15,4,4,16,26,16,4,4,16,31,31,16,4,4,16,32,42,32,16,
%T 4,4,16,32,47,47,32,16,4,4,16,32,48,58,48,32,16,4,4,16,32,48,63,63,48,
%U 32,16,4,4,16,32,48,64,74,64,48,32,16,4
%N Correlation triangle of 4-C(1,n)-2*C(0,n) (A113311).
%C Row sums are the coordination sequence for cubic lattice A005899. Diagonal sums are A115285. T(2n,n) is A113770. T(2n,n)-T(2n,n+1) is 1,6,10,10,10,.... (10-4C(1,n)-5C(0,n)).
%F G.f.: (1+x)^2*(1+x*y)^2/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*(4-C(1, k-j)-2C(0, k-j))*[j<=n-k]*((4-C(1, n-k-j)-2C(0, n-k-j))}.
%e Triangle begins
%e 1;
%e 3, 3;
%e 4, 10, 4;
%e 4, 15, 15, 4;
%e 4, 16, 26, 16, 4;
%e 4, 16, 31, 31, 16, 4;
%e 4, 16, 32, 42, 32, 16, 4;
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Jan 19 2006