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A006325
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4-dimensional analogue of centered polygonal numbers.
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19
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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
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OFFSET
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0,4
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COMMENTS
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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-subsets of X intersecting both Y and Z. - Milan Janjic, Aug 26 2007
For n>0, a(n+1) is the n-th antidiagonal sum of A213751. [Clark Kimberling, Jun 20 2012]
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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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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Milan Janjic, Two Enumerative Functions
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013
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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, Mar 14 2006
G.f.: -x^2*(x+1)^2/(x-1)^5 [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
a(n) = sum(i=1..n-1, sum (j=1..n-1, min(i,j)^2)). - Enrique Pérez Herrero, Jan 15 2013
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MATHEMATICA
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Table[n*(n-1)*(n^2-n+1)/6, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
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PROG
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(MAGMA) [n*(n-1)*(n^2-n+1)/6: n in [0..40]]; // Vincenzo Librandi, May 22 2011
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CROSSREFS
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Sequence in context: A024001 A068601 A221793 * A053346 A180669 A027964
Adjacent sequences: A006322 A006323 A006324 * 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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STATUS
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approved
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