A078990 Triangle arising from (4,2) tennis ball problem, read by rows.

1, 1, 2, 3, 1, 4, 10, 16, 22, 1, 6, 21, 52, 105, 158, 211, 1, 8, 36, 116, 301, 644, 1198, 1752, 2306, 1, 10, 55, 216, 678, 1784, 4088, 8144, 14506, 20868, 27230, 1, 12, 78, 360, 1320, 4064, 10896, 25872, 55354, 105704, 183284, 260864, 338444, 1, 14, 105

Offset: 0

Author

N. J. A. Sloane, Jan 20 2003

Keywords

• tabf
• nonn

Comments

Length of row n = 2n+1. Rows have been reversed.

Examples

			Triangle starts:
1;
1, 2,  3;
1, 4, 10, 16,  22;
1, 6, 21, 52, 105, 158, 211;
...
		

Links

• D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (Table A.1).

Crossrefs

Final diagonal gives A079489. Row sums give A066357(n+1).

Programs

PARI

T(n,k)=if(k<0 || k>2*n,0,if(n<1,k==0,sum(j=0,k,(j+1)*T(n-1,k-j))))