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 A005744 G.f.: x*(1+x-x^2)/((1-x)^4*(1+x)). (Formerly M3360) 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of n-covers of a 2-set. a(n)=A002623(n)-(n+1). Boolean switching functions a(n,s) for s = 2. Without the initial 0, this is row 1 of the convolution array A213778. - Clark Kimberling, Jun 21 2012 a(n) = A181971(n+1,n-1) for n > 0. - Reinhard Zumkeller, Jul 09 2012 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8 Vladeta Jovovic, Binary matrices up to row and column permutations Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1). FORMULA a(n) = n*(n-1)/2 + Sum((n-2*i+1)*(n-2*i)/2, i=1..floor( (n+1)/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). - R. J. Mathar, Apr 01 2010 MATHEMATICA 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 *) PROG (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 CROSSREFS John W. Layman observes that A003453 appears to be the alternating sum transform (PSumSIGN) of A005744. Cf. A002623, A005745, A005746, A005747, A005748, A005771, A003180, A052265. Sequence in context: A008023 A008055 A137441 * A027367 A009879 A219841 Adjacent sequences:  A005741 A005742 A005743 * A005745 A005746 A005747 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Additional comments from Alford Arnold STATUS approved

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Last modified January 17 17:00 EST 2018. Contains 297822 sequences.