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

0,3

Comments

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

Links

Table of n, a(n) for n=0..51.

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

Example

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

Prog

(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))))

Crossrefs

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

Sequence in context: A130152 A211233 A084608 * A176566 A079639 A104694

Adjacent sequences: A078987 A078988 A078989 * A078991 A078992 A078993

Keyword

tabf,nonn

Author

N. J. A. Sloane, Jan 20 2003

Status

approved