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, 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
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 02 2009
STATUS
approved