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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

Vladeta Jovovic, Binary matrices up to row and column permutations

Index entries for sequences related to Boolean functions

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

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

Additional comments from Alford Arnold

More terms from Vladeta Jovovic, May 25 2000

STATUS

approved

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Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.