A282081 Number of n-element subsets of [n+5] having an even sum.

1, 3, 9, 28, 66, 126, 226, 396, 651, 1001, 1491, 2184, 3108, 4284, 5796, 7752, 10197, 13167, 16797, 21252, 26598, 32890, 40326, 49140, 59423, 71253, 84903, 100688, 118728, 139128, 162248, 188496, 218025, 250971, 287793, 329004, 374794, 425334, 481194, 543004

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,-18,38,-63,84,-92,84,-63,38,-18,6,-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)^6).

a(n) = A282011(n+5,n).

a(n) = (1+n)*(2+n)*(3+n)*(4+n)*(5+n)/240 + ((-i)^n+i^n)*(8+6*n+n^2)/32 where i=sqrt(-1). - Colin Barker, Feb 06 2017

Example

a(0) = 1: {}.
a(1) = 3: {2}, {4}, {6}.
a(2) = 9: {1,3}, {1,5}, {1,7}, {2,4}, {2,6}, {3,5}, {3,7}, {4,6}, {5,7}.

Mathematica

LinearRecurrence[{6, -18, 38, -63, 84, -92, 84, -63, 38, -18, 6, -1}, {1, 3, 9, 28, 66, 126, 226, 396, 651, 1001, 1491, 2184}, 40] (* Harvey P. Dale, Sep 30 2019 *)

Prog

(PARI) Vec((x^2-x+1)*(x^4-2*x^3+6*x^2-2*x+1) / ((x^2+1)^3*(x-1)^6) + O(x^60)) \\ Colin Barker, Feb 06 2017

Crossrefs

Cf. A282011.

Sequence in context: A015638 A032092 A026524 * A022631 A027346 A325218

Adjacent sequences: A282078 A282079 A282080 * A282082 A282083 A282084

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 05 2017

Status

approved