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A329483 Number of quasi-magic (only short lines are magic) knight tours on a 4 X 2n board. 4
0, 0, 0, 4, 12, 28, 136, 488, 2624, 12420, 64120, 313584, 1675648, 8536072 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Quasi-magic tour is a special type of semi-magic tour in which the non-magic lines add to only two different values. Such tours are of interest on boards where magic tours don't exist.

LINKS

Table of n, a(n) for n=1..14.

G. P. Jelliss, Quasi-Magic Tours, The Games and Puzzles Journal #26, April-June 2003.

Awani Kumar, Studies in Tours of Knight on Rectangular Boards, arXiv:1802.09340 [math.GM], 2018.

EXAMPLE

Example of 4 x 14 quasi-magic knight tour. All short lines add to 114 and the long lines add to 397 and 401, that is 399 +- 2.

   3 56 25 32  5 52 21 36  9 48 11 40 15 44

  26 29  4 53 24 33  8 49 20 37 18 43 12 41

  55  2 31 28 51  6 35 22 47 10 39 14 45 16

  30 27 54  1 34 23 50  7 38 19 46 17 42 13

CROSSREFS

Cf. A328816, A329370.

Sequence in context: A302763 A121312 A091521 * A050898 A009845 A014342

Adjacent sequences:  A329480 A329481 A329482 * A329484 A329485 A329486

KEYWORD

nonn,hard,more

AUTHOR

Awani Kumar, Nov 14 2019

STATUS

approved

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Last modified July 9 22:46 EDT 2020. Contains 335570 sequences. (Running on oeis4.)