A115323 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n (consisting of 2n+1 terms) with [1,1,1].

1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 2, 3, 4, 5, 5, 7, 1, 3, 6, 7, 9, 12, 12, 14, 17, 1, 4, 10, 16, 17, 22, 28, 31, 33, 38, 43, 1, 5, 15, 30, 43, 43, 55, 67, 81, 81, 92, 102, 114, 1, 6, 21, 50, 88, 114, 116, 141, 165, 203, 216, 229, 254, 275, 308, 1, 7, 28, 77, 159, 252, 308, 318, 371, 422

Offset: 0

Author

Paul D. Hanna, Jan 20 2006

Keywords

• nonn
• tabl

Examples

			Convolution of [1,1,1] with row 3 gives:
[1,1,1]*[1,2,3,4,5,5,7] = [1,3,6,9,12,14,17,12,7];
when sorted yields row 4: [1,3,6,7,9,12,12,14,17].
Triangle begins:
1;
1,1,1;
1,1,2,2,3;
1,2,3,4,5,5,7;
1,3,6,7,9,12,12,14,17;
1,4,10,16,17,22,28,31,33,38,43;
1,5,15,30,43,43,55,67,81,81,92,102,114;
1,6,21,50,88,114,116,141,165,203,216,229,254,275,308;
1,7,28,77,159,252,308,318,371,422,509,583,584,648,699,758,837; ...
		

Crossrefs

Cf. A103284 (variant), A115324 (central terms), A115325 (diagonal).

Programs

PARI

T(n,k)=local(V);if(2*n=0,T(n-1,i-2))+if(i>0,T(n-1,i-1))+T(n-1,i)); V=vecsort(V);V[k+1]))