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 A159914 Half the number of (n-3)-element subsets of {1,...,n} whose elements sum up to an odd value. 3
 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; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Half the preantepenultimate column, i.e., T(n, n-3), of the triangle defined in A159916. LINKS Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018. Index entries for linear recurrences with constant coefficients, order 8, signature (4, -8, 12, -14, 12, -8, 4, -1). FORMULA 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. Euler transform of 3 - x + x^2 + 2*x^3 - x^5. - Simon Plouffe, Jun 22 2018 EXAMPLE 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}. PROG (PARI) A159914(n)=polcoeff((1-x+x^2)/(1-x)^4/(1+x^2)^2+O(x^(n-3)), n-4) CROSSREFS Cf. A228705 (counts subsets with even sum). Sequence in context: A070948 A141739 A094007 * A153251 A229167 A245968 Adjacent sequences:  A159911 A159912 A159913 * A159915 A159916 A159917 KEYWORD nonn AUTHOR M. F. Hasler, May 02 2009 STATUS approved

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Last modified March 29 14:30 EDT 2020. Contains 333107 sequences. (Running on oeis4.)