Voozh

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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).

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

EXAMPLE

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}.

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 *)

PROG

(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

CROSSREFS

Column k=9 of A282011.

Sequence in context: A275903 A273828 A147161 * A282085 A290920 A267228

Adjacent sequences: A282074 A282075 A282076 * A282078 A282079 A282080

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Feb 05 2017

STATUS

approved

URL: https://oeis.org/A282077

⇱ A282077 - OEIS