

A115292


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


4



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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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/((1x)(1x*y)(1x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*A115291(kj)*[j<=nk]*A115291(nkj)}.


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: A036605 A183541 A238389 * A202676 A173324 A318243
Adjacent sequences: A115289 A115290 A115291 * A115293 A115294 A115295


KEYWORD

easy,nonn,tabl


AUTHOR

Paul Barry, Jan 19 2006


STATUS

approved



