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

0,2

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).

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).

a(n) = floor((n+2)*(n+4)*(n+6)*(n+8)*(n^4+16*n^3+86*n^2+176*n+210)/80640 - ((n^2+n) mod 4)*(n^4+18*n^3+113*n^2+288*n+244)/768 - ((n^2+3*n) mod 4)*(2*n^3+27*n^2+112*n)/768). - Hoang Xuan Thanh, Apr 27 2026

Example

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}.

Prog

(PARI) Vec((1+10*x^2+25*x^3+15*x^4+50*x^5+100*x^6+55*x^7+55*x^8+100*x^9+50*x^10+15*x^11+25*x^12+10*x^13+x^15)/((1-x)^4*(1-x^4)^5) + O(x^40)) \\ Hoang Xuan Thanh, Apr 28 2026

Crossrefs

Cf. A282011.

Sequence in context: A246936 A110154 A158608 * A262768 A393463 A250003

Adjacent sequences: A282081 A282082 A282083 * A282085 A282086 A282087

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 05 2017

Status

approved