A282078 Number of 10-element subsets of [n+10] having an even sum.

0, 5, 30, 140, 490, 1491, 3976, 9696, 21816, 46126, 92252, 176232, 323092, 571802, 980232, 1633984, 2655224, 4217499, 6560554, 10014004, 15021006, 22174581, 32253936, 46278336, 65560976, 91786604, 127089144, 174160784, 236361064, 317866884, 423822512

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 (6,-10,-10,50,-34,-66,110,0,-110,66,34,-50,10,10,-6,1).

Formula

G.f.: -x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^11).

a(n) = (-2735775*(-1+(-1)^n) - 45*(-344851 + 56595*(-1)^n)*n + (22908402-803250*(-1)^n)*n^2 - 50*(-325607+2079*(-1)^n)*n^3 + (6781885-4725*(-1)^n)*n^4 + 1802220*n^5 + 315546*n^6 + 36300*n^7 + 2640*n^8 + 110*n^9 + 2*n^10) / 14515200. - Colin Barker, Feb 06 2017

Example

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

Prog

(PARI) concat(0, Vec(-x*(x^4+10*x^2+5)/((1+x)^5*(x-1)^11) + O(x^30))) \\ Colin Barker, Feb 06 2017

Crossrefs

Column k=10 of A282011.

Sequence in context: A213260 A054612 A358543 * A080951 A375253 A359094

Adjacent sequences: A282075 A282076 A282077 * A282079 A282080 A282081

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 05 2017

Status

approved