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Search: id:A091940
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| A091940 |
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Given n colors, sequence gives number of ways to color the vertices of a square such that no edge has the same color on both of its vertices. |
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13
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| 0, 2, 18, 84, 260, 630, 1302, 2408, 4104, 6570, 10010, 14652, 20748, 28574, 38430, 50640, 65552, 83538, 104994, 130340, 160020, 194502, 234278, 279864, 331800, 390650, 457002, 531468, 614684, 707310, 810030, 923552, 1048608, 1185954
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = 2*(n choose 2) + 12*(n choose 3) + 24*(n choose 4) = n*(n-1)*(n^2-3*n+3).
a(n+1) = n + n^4 - Rainer Rosenthal (r.rosenthal(AT)web.de), Dec 03 2006
G.f.: 2x^2(1+4x+7x^2)/(1-x)^5. a(n)=2*A027441(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]
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EXAMPLE
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a(4)=84 since there are 84 different ways to color the vertices of a square with 4 colors such that no two vertices that share an edge are the same color.
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MAPLE
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a := n -> sum((n-1)^(k^2), k=1..2); for n to 35 do a(n) end do; - Rainer Rosenthal (r.rosenthal(AT)web.de), Dec 03 2006
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MATHEMATICA
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Table[ 2Binomial[n, 2] + 12Binomial[n, 3] + 24Binomial[n, 4], {n, 35}] (from Robert G. Wilson v Mar 16 2004)
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CROSSREFS
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Sequence in context: A024171 A056664 A064057 this_sequence A068605 A070171 A036800
Adjacent sequences: A091937 A091938 A091939 this_sequence A091941 A091942 A091943
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KEYWORD
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nonn,easy
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AUTHOR
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Ryan Witko (witko(AT)nyu.edu), Mar 11 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 16 2004
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