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Search: id:A006528
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| A006528 |
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(n^4 + n^2 + 2*n)/4.
(Formerly M4160)
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+0
3
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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; listen)
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OFFSET
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0,3
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COMMENT
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Number of ways to color vertices of a square using <= n colors, allowing only rotations.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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.
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LINKS
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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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MAPLE
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A006528:=-z*(1+z+4*z**2)/(z-1)**5; [Conjectured by 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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CROSSREFS
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Sequence in context: A101854 A101877 A092348 this_sequence A052749 A090574 A080373
Adjacent sequences: A006525 A006526 A006527 this_sequence A006529 A006530 A006531
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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