A282081 Number of n-element subsets of [n+5] having an even sum.

1, 3, 9, 28, 66, 126, 226, 396, 651, 1001, 1491, 2184, 3108, 4284, 5796, 7752, 10197, 13167, 16797, 21252, 26598, 32890, 40326, 49140, 59423, 71253, 84903, 100688, 118728, 139128, 162248, 188496, 218025, 250971, 287793, 329004, 374794, 425334, 481194, 543004

Offset: 0

Author

Alois P. Heinz, Feb 05 2017

Keywords

• nonn
• easy

Examples

			a(0) = 1: {}.
a(1) = 3: {2}, {4}, {6}.
a(2) = 9: {1,3}, {1,5}, {1,7}, {2,4}, {2,6}, {3,5}, {3,7}, {4,6}, {5,7}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-18,38,-63,84,-92,84,-63,38,-18,6,-1).

Crossrefs

Cf. A282011.

Programs

Mathematica

LinearRecurrence[{6,-18,38,-63,84,-92,84,-63,38,-18,6,-1},{1,3,9,28,66,126,226,396,651,1001,1491,2184},40] (* Harvey P. Dale, Sep 30 2019 *)

PARI

Vec((x^2-x+1)*(x^4-2*x^3+6*x^2-2*x+1) / ((x^2+1)^3*(x-1)^6) + O(x^60)) \\ Colin Barker, Feb 06 2017

Formula

G.f.: (x^2-x+1)*(x^4-2*x^3+6*x^2-2*x+1)/((x^2+1)^3*(x-1)^6).

a(n) = A282011(n+5,n).

a(n) = (1+n)*(2+n)*(3+n)*(4+n)*(5+n)/240 + ((-i)^n+i^n)*(8+6*n+n^2)/32 where i=sqrt(-1). - Colin Barker, Feb 06 2017