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A224810
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Subsets of {1,2,...,n-6} without differences equal to 3 or 6.
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5
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1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 96, 144, 216, 324, 486, 729, 1053, 1521, 2197, 3211, 4693, 6859, 10108, 14896, 21952, 32144, 47068, 68921, 100860, 147600, 216000, 316800, 464640, 681472, 998976
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OFFSET
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0,8
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COMMENTS
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Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=3, r=6, I={-2,-1,1,2,3,4,5}.
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LINKS
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FORMULA
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a(n) = a(n-1) -a(n-3) +2*a(n-4) -2*a(n-6) +4*a(n-7) +2*a(n-9) +2*a(n-10) +4*a(n-12) -2*a(n-13) +2*a(n-15) -4*a(n-16) -2*a(n-18) -2*a(n-19) -a(n-21) -a(n-22) -a(n-24)
G.f.: (1+x^3-x^4-x^5+x^6-2*x^7-x^8-x^9-2*x^10-x^12-x^13-x^15) / ((1-x)*(1+x+x^2)*(1-x-x^3)*(1+3*x^3+7*x^6+9*x^9+7*x^12+3*x^15+x^18))
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MATHEMATICA
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CoefficientList[Series[(1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2017 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18))) \\ G. C. Greubel, Apr 30 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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