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A186861 Array read by antidiagonals: T(n,k) is the number of n-step king's tours on a k X k board summed over all starting positions. 7
1, 4, 0, 9, 12, 0, 16, 40, 24, 0, 25, 84, 160, 24, 0, 36, 144, 408, 496, 0, 0, 49, 220, 768, 1764, 1208, 0, 0, 64, 312, 1240, 3768, 6712, 2240, 0, 0, 81, 420, 1824, 6508, 17280, 22672, 2984, 0, 0, 100, 544, 2520, 9984, 32520, 74072, 68272, 2384, 0, 0, 121, 684 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

  1  4    9     16       25       36        49       64       81      100

  0 12   40     84      144      220       312      420      544      684

  0 24  160    408      768     1240      1824     2520     3328     4248

  0 24  496   1764     3768     6508      9984    14196    19144    24828

  0  0 1208   6712    17280    32520     52432    77016   106272   140200

  0  0 2240  22672    74072   156484    268048   408764   578632   777652

  0  0 2984  68272   296360   722384   1335984  2129440  3102752  4255920

  0  0 2384 183472  1110000  3193800   6481216 10899404 16418600 23038804

  0  0  784 436984  3908376 13530576  30543072 54738536 85743256

  0  0    0 905776 12956800 55056168 139775784

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..145

FORMULA

Empirical, for all rows: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3,3,3,5,6,7,8,9 respectively for row=1..8.

EXAMPLE

Some n=3 solutions for 3 X 3:

  3 2 0   0 0 0   0 3 0   0 0 0   0 0 0   0 0 1   0 1 0

  1 0 0   1 0 0   0 2 0   1 2 0   2 3 0   0 2 0   2 0 0

  0 0 0   2 3 0   0 0 1   3 0 0   0 1 0   0 0 3   0 3 0

CROSSREFS

Row 2 is A033586(n-1).

Sequence in context: A247127 A277896 A195056 * A187027 A187850 A186965

Adjacent sequences:  A186858 A186859 A186860 * A186862 A186863 A186864

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 27 2011

STATUS

approved

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Last modified June 19 11:11 EDT 2019. Contains 324219 sequences. (Running on oeis4.)