A282079 Number of n-element subsets of [n+2] having an even sum.

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

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1).

Formula

G.f.: -(x^4-2*x^3+4*x^2-2*x+1)/((x^2+1)^2*(x-1)^3).

a(n) = A282011(n+2,n).

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^4-2*x^3+4*x^2-2*x+1) / ((x^2+1)^2*(x-1)^3) + O(x^90)) \\ Colin Barker, Feb 06 2017

Crossrefs

Cf. A282011.

Sequence in context: A263178 A198230 A263495 * A268677 A108370 A325706

Adjacent sequences: A282076 A282077 A282078 * A282080 A282081 A282082

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 05 2017

Status

approved