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Search: id:A159914
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| A159914 |
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Half the number of (n-3)-element subsets of {1,...,n} whose elements sum up to an odd value. |
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1
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| 0, 0, 0, 0, 1, 3, 5, 8, 14, 22, 30, 40, 55, 73, 91, 112, 140, 172, 204, 240, 285, 335, 385, 440, 506, 578, 650, 728, 819, 917, 1015, 1120, 1240, 1368, 1496, 1632, 1785, 1947, 2109, 2280, 2470, 2670, 2870, 3080, 3311, 3553, 3795, 4048, 4324, 4612, 4900, 5200
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Half the preantepenultimate column, i.e. T[n,n-3], of the triangle defined in A159916.
This is a linear recurring sequence with constant coefficients and characteristic polynomial x^8 - 4*x^7 + 8*x^6 - 12*x^5 + 14*x^4 - 12*x^3 + 8*x^2 - 4*x + 1 = (x-1)^4 (x^2+1)^2?
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FORMULA
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G.f.: x^4 (1-x+x^2) (1-x)^-4 (1+x^2)^-2.
a(n) = A159916(n(n-1)/2+n-3)/2 = T[n,n-3]/2 as defined there.
a(2k) = k(k-1)(2k-1)/6
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EXAMPLE
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The first nontrivial term a(4)=1 is half the number of 4-3=1-element subsets of {1,2,3,4} whose elements have an odd sum: {1} and {3}.
a(5)=3 is half the number of 5-3=2-element subsets of {1,2,3,4,5} whose elements have an odd sum: {1,2}, {1,4}, {2,3}, {2,5}, {3,4} and {4,5}.
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PROGRAM
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(PARI) A159914(n)=polcoeff((1-x+x^2)/(1-x)^4/(1+x^2)^2+O(x^(n-3)), n-4)
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CROSSREFS
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Sequence in context: A070948 A141739 A094007 this_sequence A153251 A109022 A023596
Adjacent sequences: A159911 A159912 A159913 this_sequence A159915 A159916 A159917
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 02 2009
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