A159914 Half the number of (n-3)-element subsets of {1,...,n} whose elements sum up to an odd value.

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

Offset

0,6

Comments

Half the preantepenultimate column, i.e., T(n, n-3), of the triangle defined in A159916.

Links

Table of n, a(n) for n=0..51.

Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Index entries for linear recurrences with constant coefficients, 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: A352087 A141739 A094007 * A153251 A229167 A245968

Adjacent sequences: A159911 A159912 A159913 * A159915 A159916 A159917

Keyword

nonn

Author

M. F. Hasler, May 02 2009

Status

approved