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
Keywords
Examples
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}.
Links
- 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).
Crossrefs
Cf. A228705 (counts subsets with even sum).
Programs
-
PARI
A159914(n)=polcoeff((1-x+x^2)/(1-x)^4/(1+x^2)^2+O(x^(n-3)),n-4)
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
Comments