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A366829
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Number of 9-step self-avoiding king's tours on an n X n board summed over all starting positions.
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1
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0, 0, 784, 436984, 3908376, 13530576, 30543072, 54738536, 85743256, 123447704, 167851880, 218955784, 276759416, 341262776, 412465864, 490368680, 574971224, 666273496, 764275496, 868977224, 980378680, 1098479864, 1223280776, 1354781416, 1492981784, 1637881880
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OFFSET
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1,3
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COMMENTS
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Distribution matrix of surrounding rectangles for 9-step walks is:
[0 0 0 0 0 0 0 0 2]
[0 0 0 0 3584 10496 10752 5120 1020]
[0 0 784 43856 129100 136320 83208 29160 4680]
[0 0 43856 258424 318816 215096 99984 29680 4296]
[0 3584 129100 318816 262816 142888 57376 15400 2100]
[0 10496 136320 215096 142888 67688 24288 5960 768]
[0 10752 83208 99984 57376 24288 7864 1760 212]
[0 5120 29160 29680 15400 5960 1760 360 40]
[2 1020 4680 4296 2100 768 212 40 4]
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LINKS
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FORMULA
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a(n) = 3349864*n^2 - 25942968*n + 47890984 for n>7.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 10. - Stefano Spezia, Oct 28 2023
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EXAMPLE
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Some solutions for 3 X 3:
1 2 3 1 2 3 1 2 3 1 2 3 1 7 8 1 2 8
4 5 6 6 5 4 8 9 4 7 6 4 6 2 9 3 7 9
7 8 9 7 8 9 7 6 5 8 9 5 5 4 3 4 5 6
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CROSSREFS
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KEYWORD
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nonn,easy,walk
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AUTHOR
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STATUS
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approved
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