A114972 Array read by antidiagonals: consider a doubly infinite chessboard with squares labeled (i,j), i in Z, j in Z; T(i,j) = number of king-paths of length max{i,j} from (0,0) to (i,j).

1, 1, 1, 3, 1, 3, 7, 2, 2, 7, 19, 6, 1, 6, 19, 51, 16, 3, 3, 16, 51, 141, 45, 10, 1, 10, 45, 141, 393, 126, 30, 4, 4, 30, 126, 393, 1107, 357, 90, 15, 1, 15, 90, 357, 1107, 3139, 1016, 266, 50, 5, 5, 50, 266, 1016, 3139, 8953, 2907, 784, 161, 21, 1, 21, 161, 784, 2907

Offset: 0

Author

N. J. A. Sloane, based on May 27 2005 email from Harrie Grondijs, Feb 27 2006

Keywords

• nonn
• tabl
• easy

Examples

			Array begins:
1 1 3 7 19 ...
1 1 2 6 ...
3 2 1 3 ...
7 6 3 1 ...
...
		

References

• Harrie Grondijs, Neverending Quest of Type C, Volume B - the endgame study-as-struggle.

Crossrefs

Cf. A111808, A026300, A114929.

Formula

Equals triangle A111808 next to same triangle reflected in mirror. See A111808 for obvious recurrence.

Extensions

More terms from Joshua Zucker, May 20 2006

T(0,0) corrected by Johannes W. Meijer, Oct 05 2010