A115292 Correlation triangle for (1+x)^3/(1-x).

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, 40, 8, 8, 40, 96, 152, 152, 96, 40, 8, 8, 40, 96, 159, 194, 159, 96, 40, 8, 8, 40, 96, 160, 216, 216, 160, 96, 40, 8, 8, 40, 96, 160, 223, 258, 223, 160, 96, 40, 8

Offset

0,2

Comments

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,...

Links

Table of n, a(n) for n=0..65.

Formula

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)}.

Example

Triangle begins
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, 40, 8;
8, 40, 96, 152, 152, 96, 40, 8;

Crossrefs

Sequence in context: A183541 A323657 A238389 * A202676 A330765 A336718

Adjacent sequences: A115289 A115290 A115291 * A115293 A115294 A115295

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 19 2006

Status

approved