A114929 Array read by antidiagonals: consider a semi-infinite chessboard with squares labeled (i,j), i >= 0, j >= 0; T(i,j) = number of king-paths of length max{i,j} from (0,0) to (i,j).

1, 1, 1, 2, 1, 2, 4, 2, 2, 4, 9, 5, 1, 5, 9, 21, 12, 3, 3, 12, 21, 51, 30, 9, 1, 9, 30, 51, 127, 76, 25, 4, 4, 25, 76, 127, 323, 196, 69, 14, 1, 14, 69, 196, 323, 835, 512, 189, 44, 5, 5, 44, 189, 512, 835, 2188, 1353, 518, 133, 20, 1, 20, 133, 518, 1353, 2188, 5798, 3610, 1422

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 2 4 9 21 51 ...
1 1 2 5 12 30 ...
2 2 1 3 9 25 ...
4 5 3 1 4 14 ...
...
		

References

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

Crossrefs

Cf. A026300, A020474, A111808, A114972.

Formula

Equals Motzkin triangle (A026300) next to same triangle reflected in mirror. See A026300 for the obvious recurrence.

Extensions

More terms from Joshua Zucker, May 20 2006

T(0,0) corrected by Johannes W. Meijer, Oct 07 2010