OFFSET
0,3
COMMENTS
FORMULA
EXAMPLE
Triangle begins:
1;
1, 2;
3, 3, 5;
6, 11, 8, 11;
17, 25, 30, 19, 28;
42, 72, 74, 77, 47, 70;
114, 188, 223, 198, 194, 117, 184;
302, 525, 609, 615, 509, 495, 301, 486;
827, 1436, 1749, 1733, 1619, 1305, 1282, 787, 1313;
2263, 4012, 4918, 5101, 4657, 4206, 3374, 3382, 2100, 3576;
6275, 11193, 14031, 14676, 13964, 12237, 10962, 8856, 9058, 5676, 9851;
The convolution of each row with [1,1,1] yields:
[1,1,1]*[1] = [1,1,1];
[1,1,1]*[1,2] = [1,3,3,2];
[1,1,1]*[3,3,5] = [3,6,11,8,5];
[1,1,1]*[6,11,8,11] = [6,17,25,30,19,11]; ...
Concatenate these convoluted rows after adding last and first terms:
1,1,1 + 1,3,3,2 + 3,6,11,8,5 + 6,17,25,30,19,11 + 17, ...
to obtain the concatenated rows of this original triangle:
1, 1,2, 3,3,5, 6,11,8,11, 17,25,30,19,28, ...
PROG
(PARI) {T(n, k)=if(n<k||k<0, 0, if(n==0&k==0, 1, if(n==k, T(n, 0)+T(n-1, n-1), T(n-1, k-1)+T(n-1, k)+T(n-1, k+1))))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Jul 27 2006
STATUS
approved