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A182406
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Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the square grid graph G_(k,k).
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28
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1, 0, 2, 0, 2, 3, 0, 2, 18, 4, 0, 2, 246, 84, 5, 0, 2, 7812, 9612, 260, 6, 0, 2, 580986, 6000732, 142820, 630, 7, 0, 2, 101596896, 20442892764, 828850160, 1166910, 1302, 8, 0, 2, 41869995708, 380053267505964, 50820390410180, 38128724910, 6464682, 2408, 9
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OFFSET
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1,3
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COMMENTS
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The square grid graph G_(n,n) has n^2 = A000290(n) vertices and 2*n*(n-1) = A046092(n-1) edges. The chromatic polynomial of G_(n,n) has n^2+1 = A002522(n) coefficients.
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LINKS
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EXAMPLE
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Square array A(n,k) begins:
1, 0, 0, 0, 0, ...
2, 2, 2, 2, 2, ...
3, 18, 246, 7812, 580986, ...
4, 84, 9612, 6000732, 20442892764, ...
5, 260, 142820, 828850160, 50820390410180, ...
6, 630, 1166910, 38128724910, 21977869327169310, ...
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CROSSREFS
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Rows n=1-20 give: A000007, A007395, A068253*3, A068254*4, A068255*5, A068256*6, A068257*7, A068258*8, A068259*9, A068260*10, A068261*11, A068262*12, A068263*13, A068264*14, A068265*15, A068266*16, A068267*17, A068268*18, A068269*19, A068270*20.
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KEYWORD
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AUTHOR
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STATUS
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approved
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