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A039623
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Consider a figure like this <> (a squashed square, symmetric about both axes); each side is given 1 of n colors; a(n) = number of possibilities, allowing turning over.
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5
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1, 7, 27, 76, 175, 351, 637, 1072, 1701, 2575, 3751, 5292, 7267, 9751, 12825, 16576, 21097, 26487, 32851, 40300, 48951, 58927, 70357, 83376, 98125, 114751, 133407, 154252, 177451, 203175, 231601, 262912, 297297, 334951, 376075, 420876, 469567
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 2 X 2 matrices with entries mod n, up to row and column permutation. Number of k X l matrices with entries mod n, up to row and column permutation is Z(S_k X S_l; n,n,...) where Z(S_k X S_l; x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_k and S_l of degree k and l, respectively - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 04 2000
If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-5) is the number of 6-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Sep 08 2007
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REFERENCES
| J.-P. Delahaye, 'Le miraculeux "lemme de Burnside"','Le matelas a k couleurs' pp 145-6 in 'Pour la Science' (French edition of 'Scientific American') No.350 December 2006 Paris.
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LINKS
| Milan Janjic, Two Enumerative Functions
Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n)=(1/4)*n^2*(n^2+3).
a(1)=1, a(2)=7, a(3)=27, a(4)=76, a(5)=175, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Oct 01 2011]
G.f.: (-1-2*x-2*x^2-x^3)/(x-1)^5 [From Harvey P. Dale, Oct 01 2011]
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EXAMPLE
| a(1)=1, a(4)=76.
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MATHEMATICA
| Table[(n^2 (n^2+3))/4, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 7, 27, 76, 175}, 40] (* From Harvey P. Dale, Oct 01 2011 *)
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CROSSREFS
| Cf. A058001-A058004, A002724, A052271, A052272, A005353.
Sequence in context: A143690 A007715 A161439 * A162210 A161716 A162493
Adjacent sequences: A039620 A039621 A039622 * A039624 A039625 A039626
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Christian Meland (christian.meland(AT)pfi.no)
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EXTENSIONS
| More terms from Sam Alexander (pink2001x(AT)hotmail.com)
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