A282080 Number of n-element subsets of [n+4] having an even sum.

1, 2, 6, 19, 38, 60, 100, 170, 255, 350, 490, 693, 924, 1176, 1512, 1956, 2445, 2970, 3630, 4455, 5346, 6292, 7436, 8814, 10283, 11830, 13650, 15785, 18040, 20400, 23120, 26248, 29529, 32946, 36822, 41211, 45790, 50540, 55860, 61810, 67991, 74382, 81466, 89309

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,-13,25,-38,46,-46,38,-25,13,-5,1).

Formula

G.f.: -(x^2-x+1)*(x^4-2*x^3+6*x^2-2*x+1)/((x^2+1)^3*(x-1)^5).

a(n) = A282011(n+4,n).

a(n) = (2*(1+n)*(2+n)*(3+n)*(4+n) + 3*(-i*(-i)^n*((3+8*i) + (4+6*i)*n + (1+i)*n^2) + i^n*((8+3*i) + (6+4*i)*n + (1+i)*n^2)))/96 where i=sqrt(-1). - Colin Barker, Feb 06 2017

Example

a(2) = 6: {1,3}, {1,5}, {2,4}, {2,6}, {3,5}, {4,6}.
a(3) = 19: {1,2,3}, {1,2,5}, {1,2,7}, {1,3,4}, {1,3,6}, {1,4,5}, {1,4,7}, {1,5,6}, {1,6,7}, {2,3,5}, {2,3,7}, {2,4,6}, {2,5,7}, {3,4,5}, {3,4,7}, {3,5,6}, {3,6,7}, {4,5,7}, {5,6,7}.

Mathematica

CoefficientList[Series[-(x^2 - x + 1)*(x^4 - 2*x^3 + 6*x^2 - 2*x + 1)/((x^2 + 1)^3*(x - 1)^5), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 01 2024 *)

Prog

(PARI) Vec(-(x^2-x+1)*(x^4-2*x^3+6*x^2-2*x+1)/((x^2+1)^3*(x-1)^5) + O(x^90)) \\ Colin Barker, Feb 06 2017

Crossrefs

Cf. A282011.

Sequence in context: A227884 A186769 A213400 * A273180 A280041 A058081

Adjacent sequences: A282077 A282078 A282079 * A282081 A282082 A282083

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 05 2017

Status

approved