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A183048
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Sums of least number of knight's moves on boundaries of squares [-n,n]x[-n,n] on infinite chessboard.
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1
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0, 20, 32, 60, 88, 140, 184, 260, 312, 412, 480, 596, 680, 820, 912, 1076, 1184, 1364, 1488, 1692, 1824, 2052, 2200, 2444, 2608, 2876, 3048, 3340, 3528, 3836, 4040, 4372, 4584, 4940, 5168, 5540, 5784, 6180, 6432
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OFFSET
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0,2
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COMMENTS
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First difference sequence of A183047.
Every term is divisible by 4.
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LINKS
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FORMULA
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Empirical g.f.: 4*x*(2*x^8+2*x^7-4*x^6-5*x^5-2*x^4-x^3-5*x^2-8*x-5) / ((x-1)^3*(x+1)^2*(x^2+x+1)). - Colin Barker, May 04 2014
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EXAMPLE
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Start with the square [-2,2]x[2,2],
4 1 2 1 4
1 2 3 2 1
2 3 0 3 2
1 2 3 2 1
4 1 2 1 4,
remove the square [-1,1]x[-1,1],
2 3 4
3 0 3
2 3 2,
and then add the remaining numbers:
4+1+2+1+4+1+2+1+4+1+2+1+4+1+2+1
to get a(2)=32.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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