

A282079


Number of nelement subsets of [n+2] having an even sum.


2



1, 1, 2, 6, 9, 9, 12, 20, 25, 25, 30, 42, 49, 49, 56, 72, 81, 81, 90, 110, 121, 121, 132, 156, 169, 169, 182, 210, 225, 225, 240, 272, 289, 289, 306, 342, 361, 361, 380, 420, 441, 441, 462, 506, 529, 529, 552, 600, 625, 625, 650, 702, 729, 729, 756, 812, 841
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OFFSET

0,3


LINKS



FORMULA

G.f.: (x^42*x^3+4*x^22*x+1)/((x^2+1)^2*(x1)^3).
a(n) = (2*(1+n)*(2+n)  i*(i)^n*((1+2*i)+(1+i)*n) + i^n*((2+i)+(1+i)*n))/8 where i=sqrt(1).  Colin Barker, Feb 06 2017


EXAMPLE

a(3) = 6: {1,2,3}, {1,2,5}, {1,3,4}, {1,4,5}, {2,3,5}, {3,4,5}.
a(4) = 9: {1,2,3,4}, {1,2,3,6}, {1,2,4,5}, {1,2,5,6}, {1,3,4,6}, {1,4,5,6}, {2,3,4,5}, {2,3,5,6}, {3,4,5,6}.


PROG

(PARI) Vec((x^42*x^3+4*x^22*x+1) / ((x^2+1)^2*(x1)^3) + O(x^90)) \\ Colin Barker, Feb 06 2017


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



