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

0,4

References

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

Links

Table of n, a(n) for n=0..68.

Formula

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

Example

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 ...
...

Crossrefs

Cf. A026300, A020474, A111808, A114972.

Sequence in context: A270594 A270706 A082793 * A247321 A152251 A144025

Adjacent sequences: A114926 A114927 A114928 * A114930 A114931 A114932

Keyword

nonn,tabl,easy

Author

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

Extensions

More terms from Joshua Zucker, May 20 2006

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

Status

approved