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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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Feb 05 2017
STATUS
approved

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Last modified May 22 09:57 EDT 2024. Contains 372745 sequences. (Running on oeis4.)