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Correlation triangle for (1+x)^3/(1-x).
4

%I #3 Mar 30 2012 18:59:13

%S 1,4,4,7,17,7,8,32,32,8,8,39,66,39,8,8,40,88,88,40,8,8,40,95,130,95,

%T 40,8,8,40,96,152,152,96,40,8,8,40,96,159,194,159,96,40,8,8,40,96,160,

%U 216,216,160,96,40,8,8,40,96,160,223,258,223,160,96,40,8

%N Correlation triangle for (1+x)^3/(1-x).

%C Row sums are A115293. Diagonal sums are A115294. T(2n,n) is A115295. T(2n,n)-T(2n,n+1) is 1,10,27,35,35,35,... The transform of (-1)^n by this matrix is 1,0,-3,0,4,0,-4,0,4,...

%F G.f.: (1+x)^3*(1+xy)^3/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*A115291(k-j)*[j<=n-k]*A115291(n-k-j)}.

%e Triangle begins

%e 1;

%e 4, 4;

%e 7, 17, 7;

%e 8, 32, 32, 8;

%e 8, 39, 66, 39, 8;

%e 8, 40, 88, 88, 40, 8;

%e 8, 40, 95, 130, 95, 40, 8;

%e 8, 40, 96, 152, 152, 96, 40, 8;

%K easy,nonn,tabl

%O 0,2

%A _Paul Barry_, Jan 19 2006