A282077 Number of 9-element subsets of [n+9] having an even sum.

0, 5, 25, 110, 350, 1001, 2485, 5720, 12120, 24310, 46126, 83980, 146860, 248710, 408430, 653752, 1021240, 1562275, 2343055, 3453450, 5007002, 7153575, 10079355, 14024400, 19282640, 26225628, 35302540, 47071640, 62200280, 81505820, 105955628, 136719440

Offset: 0

Author

Alois P. Heinz, Feb 05 2017

Keywords

• nonn
• easy

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-5,-15,35,1,-65,45,45,-65,1,35,-15,-5,5,-1).

Crossrefs

Column k=9 of A282011.

Programs

Mathematica

LinearRecurrence[{5,-5,-15,35,1,-65,45,45,-65,1,35,-15,-5,5,-1},{0,5,25,110,350,1001,2485,5720,12120,24310,46126,83980,146860,248710,408430},40] (* Harvey P. Dale, Jun 10 2018 *)

PARI

concat(0, Vec(x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^10) + O(x^30))) \\ Colin Barker, Feb 06 2017

Formula

G.f.: x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^10).

a(n) = ((384 + 400*n + 140*n^2 + 20*n^3 + n^4)*(-945*(-1+(-1)^n) + 3378*n + 1900*n^2 + 460*n^3 + 50*n^4 + 2*n^5)) / 1451520. - Colin Barker, Feb 06 2017