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A006528
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(n^4 + n^2 + 2*n)/4.
(Formerly M4160)
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5
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0, 1, 6, 24, 70, 165, 336, 616, 1044, 1665, 2530, 3696, 5226, 7189, 9660, 12720, 16456, 20961, 26334, 32680, 40110, 48741, 58696, 70104, 83100, 97825, 114426, 133056, 153874, 177045, 202740, 231136, 262416, 296769, 334390, 375480
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of ways to color vertices of a square using <= n colors, allowing only rotations.
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REFERENCES
| Nick Baxter, The Burnside di-lemma: combinatorics and puzzle symmetry, in Tribute to a Mathemagician, Peters, 2005, pp. 199-210.
M. Gardner, New Mathematical Diversions from Scientific American. Simon and Schuster, NY, 1966, p. 246.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| a(n) = n*(n+1)*(n^2-n+2)/4.
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MAPLE
| A006528:=-z*(1+z+4*z**2)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]
a:=n->add(n+add(binomial(n, 2), j=1..n), j=0..n):seq(a(n)/2, n=0..35); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 26 2008]
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MATHEMATICA
| Table[CycleIndex[CyclicGroup[4], t]/.Table[t[i]->n, {i, 1, 4}], {n, 0, 20}] (* Geoffrey Critzer, Mar 13 2011*)
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CROSSREFS
| Cf. A002817 (square colorings).
Sequence in context: A101854 A101877 A092348 * A052749 A090574 A080373
Adjacent sequences: A006525 A006526 A006527 * A006529 A006530 A006531
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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