A282084 Number of n-element subsets of [n+8] having an even sum.

1, 4, 20, 85, 255, 636, 1484, 3235, 6470, 12120, 21816, 37854, 63090, 101640, 159720, 245322, 367983, 540540, 780780, 1110395, 1554553, 2145572, 2925780, 3945045, 5260060, 6941168, 9076912, 11769100, 15131700, 19302480, 24449808, 30763812, 38454765, 47771700

Offset: 0

Author

Alois P. Heinz, Feb 05 2017

Keywords

• nonn
• easy

Examples

			a(0) = 1: {}.
a(1) = 4: {2}, {4}, {6}, {8}.
a(2) = 20: {1,3}, {1,5}, {1,7}, {1,9}, {2,4}, {2,6}, {2,8}, {2,10}, {3,5}, {3,7}, {3,9}, {4,6}, {4,8}, {4,10}, {5,7}, {5,9}, {6,8}, {6,10}, {7,9}, {8,10}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -41, 129, -316, 636, -1084, 1596, -2054, 2326, -2326, 2054, -1596, 1084, -636, 316, -129, 41, -9, 1).

Crossrefs

Cf. A282011.

Formula

G.f.: -(x^2-x+1)*(x^8-4*x^7+20*x^6-36*x^5+54*x^4-36*x^3+20*x^2-4*x+1) / ((x^2+1)^5*(x-1)^9).

a(n) = A282011(n+8,n).