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A005744
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Expansion of x*(1+x-x^2)/((1-x)^4*(1+x)).
(Formerly M3360)
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13
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0, 1, 4, 9, 17, 28, 43, 62, 86, 115, 150, 191, 239, 294, 357, 428, 508, 597, 696, 805, 925, 1056, 1199, 1354, 1522, 1703, 1898, 2107, 2331, 2570, 2825, 3096, 3384, 3689, 4012, 4353, 4713, 5092, 5491, 5910, 6350, 6811, 7294, 7799, 8327, 8878, 9453, 10052
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OFFSET
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0,3
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COMMENTS
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Number of n-covers of a 2-set.
Boolean switching functions a(n,s) for s = 2.
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REFERENCES
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R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = n*(n-1)/2 + Sum_{j=1..floor((n+1)/2)} (n-2*j+1)*(n-2*j)/2. - N. J. A. Sloane, Nov 28 2003
a(n) = 5*n/12 - 1/16 + 5*n^2/8 + n^3/12 + (-1)^n/16.
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5). (End)
E.g.f.: (x*(2*x^2 + 21*x + 27)*cosh(x) + (2*x^3 + 21*x^2 + 27*x - 3)*sinh(x))/24. - Stefano Spezia, Jul 27 2022
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MATHEMATICA
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CoefficientList[Series[x (1+x-x^2)/((1-x)^4(1+x)), {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -2, -2, 3, -1}, {0, 1, 4, 9, 17}, 50] (* Harvey P. Dale, Apr 10 2012 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 3, -2, -2, 3]^n*[0; 1; 4; 9; 17])[1, 1] \\ Charles R Greathouse IV, Feb 06 2017
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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