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A282079 Number of n-element subsets of [n+2] having an even sum. 2
1, 1, 2, 6, 9, 9, 12, 20, 25, 25, 30, 42, 49, 49, 56, 72, 81, 81, 90, 110, 121, 121, 132, 156, 169, 169, 182, 210, 225, 225, 240, 272, 289, 289, 306, 342, 361, 361, 380, 420, 441, 441, 462, 506, 529, 529, 552, 600, 625, 625, 650, 702, 729, 729, 756, 812, 841 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1).

FORMULA

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

a(n) = A282011(n+2,n).

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

EXAMPLE

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

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

PROG

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

CROSSREFS

Cf. A282011.

Sequence in context: A263178 A198230 A263495 * A121248 A268677 A108370

Adjacent sequences:  A282076 A282077 A282078 * A282080 A282081 A282082

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Feb 05 2017

STATUS

approved

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Last modified September 28 07:55 EDT 2020. Contains 337394 sequences. (Running on oeis4.)