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A005746 Number of n-covers of a 4-set.
(Formerly M4634)
4
1, 9, 51, 230, 863, 2864, 8609, 23883, 61883, 151214, 350929, 778113, 1656265, 3398229, 6743791, 12983181, 24311044, 44377016, 79124476, 138048542, 236050912, 396137492, 653285736, 1059923072, 1693592112, 2667563553, 4145373780, 6360553548, 9643151582 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.

Vladeta Jovovic, Binary matrices up to row and column permutations

FORMULA

a(n) = A006148(n) - A002727(n).

G.f.: x*(1 +3*x +9*x^2 +26*x^3 +35*x^4 +92*x^5 +127*x^6 +201*x^7 +242*x^8 +253*x^9 +248*x^10 +205*x^11 +123*x^12 +86*x^13 +31*x^14 +24*x^15 +19*x^16 +5*x^17 +3*x^18 -2*x^19 -4*x^20 +2*x^21 -4*x^22 +3*x^23 -x^25 +2*x^26 -x^27) / ((1 -x)^16*(1 +x)^6*(1 +x^2)^3*(1 +x +x^2)^4). - Corrected by Colin Barker, Aug 23 2016

MATHEMATICA

Rest@ CoefficientList[Series[x (1 + 3 x + 9 x^2 + 26 x^3 + 35 x^4 + 92 x^5 + 127 x^6 + 201 x^7 + 242 x^8 + 253 x^9 + 248 x^10 + 205 x^11 + 123 x^12 + 86 x^13 + 31 x^14 + 24 x^15 + 19 x^16 + 5 x^17 + 3 x^18 -

2 x^19 - 4 x^20 + 2 x^21 - 4 x^22 + 3 x^23 - x^25 + 2 x^26 - x^27)/((1 - x)^16 (1 + x)^6 (1 + x^2)^3 (1 + x + x^2)^4), {x, 0, 29}], x] (* Michael De Vlieger, Aug 23 2016 *)

PROG

(PARI) Vec(x*(1 +3*x +9*x^2 +26*x^3 +35*x^4 +92*x^5 +127*x^6 +201*x^7 +242*x^8 +253*x^9 +248*x^10 +205*x^11 +123*x^12 +86*x^13 +31*x^14 +24*x^15 +19*x^16 +5*x^17 +3*x^18 -2*x^19 -4*x^20 +2*x^21 -4*x^22 +3*x^23 -x^25 +2*x^26 -x^27) / ((1 -x)^16*(1 +x)^6*(1 +x^2)^3*(1 +x +x^2)^4) + O(x^40)) \\ Colin Barker, Aug 23 2016

CROSSREFS

Cf. A005744, A005745, A005747, A005748, A005771.

Sequence in context: A282877 A055900 A054549 * A220236 A061178 A246178

Adjacent sequences:  A005743 A005744 A005745 * A005747 A005748 A005749

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

More terms and g.f. from Vladeta Jovovic, May 26 2000

a(19) onwards corrected by Sean A. Irvine, Aug 22 2016

STATUS

approved

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Last modified November 16 04:54 EST 2018. Contains 317257 sequences. (Running on oeis4.)