A057790 Table read by antidiagonals: T(n,k) = number of restricted knight's walks from (n,k) (n >= 0, k >= 0).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 3, 4, 4, 3, 1, 1, 1, 1, 5, 5, 6, 5, 5, 1, 1, 1, 1, 6, 7, 10, 10, 7, 6, 1, 1, 1, 1, 8, 11, 16, 14, 16, 11, 8, 1, 1, 1, 1, 12, 17, 22, 27, 27, 22, 17, 12, 1, 1, 1, 1, 18, 23, 39, 44, 44, 44, 39, 23, 18, 1, 1, 1, 1

Offset

0,13

Comments

Moves are restricted to be (-2,1) or (1,-2), and end when either coordinate is < 2.

Links

Table of n, a(n) for n=0..92.

M. Bousquet-Mélou and M. Petkovsek, Linear recurrences with constant coefficients: the multivariate case, Preprint 687, Volume 38 (2000), Preprint Series of the Institute of Mathematics, Physics and Mechanics of Ljubljana.

M. Bousquet-Mélou and M. Petkovsek, Walks confined in a quadrant are not always D-finite, arXiv:math/0211432 [math.CO], 2002.

Example

The table starts:
  1  1  1  1  1  1
  1  1  1  1  1  1
  1  1  2  2  3  3
  1  1  2  2  4  5
  1  1  3  4  6 10
  1  1  3  5 10 14

Maple

T:=proc(n, k) if n=0 or n=1 or k=0 or k=1 then 1 else T(n+1, k-2)+T(n-2, k+1) fi end: seq(seq(T(n, s-n), n=0..s), s=0..15);

Mathematica

t[n_, k_] := t[n, k] = If[ n == 0 || n == 1 || k == 0 || k == 1, 1, t[n + 1, k - 2] + t[n - 2, k + 1]]; Table[t[n, s - n], {s, 0, 13}, {n, 0, s}] // Flatten (* Jean-François Alcover, Jan 29 2013, translated from Maple *)

Crossrefs

Sequence in context: A155050 A140356 A119963 * A350889 A224697 A052307

Adjacent sequences: A057787 A057788 A057789 * A057791 A057792 A057793

Keyword

nonn,tabl,easy,nice

Author

N. J. A. Sloane, Nov 05 2000

Extensions

More terms from Emeric Deutsch, May 23 2004

Definition clarified by Franklin T. Adams-Watters, Jun 12 2014

Status

approved