A282085 Number of n-element subsets of [n+9] having an even sum.

1, 5, 25, 110, 365, 1001, 2485, 5720, 12190, 24310, 46126, 83980, 147070, 248710, 408430, 653752, 1021735, 1562275, 2343055, 3453450, 5008003, 7153575, 10079355, 14024400, 19284460, 26225628, 35302540, 47071640, 62203340, 81505820, 105955628, 136719440

Offset: 0

Author

Alois P. Heinz, Feb 05 2017

Keywords

• nonn
• easy

Examples

			a(0) = 1: {}.
a(1) = 5: {2}, {4}, {6}, {8}, {10}.
a(2) = 25: {1,3}, {1,5}, {1,7}, {1,9}, {1,11}, {2,4}, {2,6}, {2,8}, {2,10}, {3,5}, {3,7}, {3,9}, {3,11}, {4,6}, {4,8}, {4,10}, {5,7}, {5,9}, {5,11}, {6,8}, {6,10}, {7,9}, {7,11}, {8,10}, {9,11}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10, -50, 170, -445, 952, -1720, 2680, -3650, 4380, -4652, 4380, -3650, 2680, -1720, 952, -445, 170, -50, 10, -1).

Crossrefs

Cf. A282011.

Programs

Mathematica

T[n_, k_] := Sum[Binomial[Ceiling[n/2], 2 j] Binomial[Floor[n/2], k - 2 j], {j, 0, Floor[(n + 1)/4]}]; Table[T[n + 9, n], {n, 0, 31}] (* or *) CoefficientList[Series[(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)^10), {x, 0, 31}], x] (* Indranil Ghosh, Feb 26 2017 *)

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)^10).

a(n) = A282011(n+9,n).