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Search: id:A006325
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| A006325 |
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4-dimensional analogue of centered polygonal numbers. |
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+0
12
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| 0, 0, 1, 7, 26, 70, 155, 301, 532, 876, 1365, 2035, 2926, 4082, 5551, 7385, 9640, 12376, 15657, 19551, 24130, 29470, 35651, 42757, 50876, 60100, 70525, 82251, 95382, 110026, 126295, 144305, 164176, 186032, 210001, 236215, 264810, 295926
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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If X is an n-set and Y and Z disjoint 2-subsets of X then a(n-4) is equal to the number of 6-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Aug 26 2007
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REFERENCES
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T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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a(n) = n*(n-1)*(n^2-n+1)/6.
a(n) = [(n^5-(n-1)^5)-(n^1-(n-1)^1)]/30 = (n^5-(n-1)^5-1)/30. - Xavier Acloque Jan 25 2003
This sequence is, with different offset, the partial sums of the octahedral numbers. a(n+1) = SUM[i=0..n] A005900(i). a(n+1) = SUM[i=0..n] OctahedralNumber(i). a(n+1) = SUM[i=0..n] (2n^3 + n)/3. - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 14 2006
G.f.:-x^2*(x+1)^2/(x-1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
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CROSSREFS
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Sequence in context: A135300 A024001 A068601 this_sequence A053346 A027964 A078501
Adjacent sequences: A006322 A006323 A006324 this_sequence A006326 A006327 A006328
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KEYWORD
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nonn,easy
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AUTHOR
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Albert Rich (Albert_Rich(AT)msn.com)
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