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A282080
Number of n-element subsets of [n+4] having an even sum.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Feb 05 2017
STATUS
approved