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

0,4

References

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

Links

Table of n, a(n) for n=0..64.

Formula

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

Example

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

Crossrefs

Cf. A111808, A026300, A114929.

Sequence in context: A208916 A209766 A356207 * A107461 A035619 A280995

Adjacent sequences: A114969 A114970 A114971 * A114973 A114974 A114975

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 05 2010

Status

approved