

A007387


Number of 3rdorder maximal independent sets in cycle graph.
(Formerly M0426)


5



0, 2, 3, 2, 5, 2, 7, 2, 9, 7, 11, 14, 13, 23, 20, 34, 34, 47, 57, 67, 91, 101, 138, 158, 205, 249, 306, 387, 464, 592, 713, 898, 1100, 1362, 1692, 2075, 2590, 3175, 3952, 4867, 6027, 7457, 9202, 11409, 14069, 17436, 21526, 26638, 32935, 40707, 50371, 62233
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OFFSET

1,2


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. Yanco and A. Bagchi, "Kth order maximal independent sets in path and cycle graphs," J. Graph Theory, submitted, 1994.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
R. Yanco, Letter and Email to N. J. A. Sloane, 1994
R. Yanco and A. Bagchi, Kth order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy)


FORMULA

For n >= 9: a(n) = a(n2) + a(n5) per A133394.  G. Reed Jameson (Reedjameson(AT)yahoo.com), Dec 13 2007, Dec 16 2007
G.f.: x^2*(2 + 3*x + 2*x^3  3*x^6)/(1  x^2  x^5).  R. J. Mathar, Oct 30 2009
a(n) = Sum_{j=0..floor((ng)/(2*g))} (2*n/(n2*(g2)*j(g2))) * Hypergeometric2F1([(n2g*jg)/2,(2j+1)], [1], 1), with g = 5, n >= g, and n an odd integer.  Richard Turk, Oct 14 2019


MAPLE

seq(coeff(series(x^2*(2+3*x+2*x^33*x^6)/(1x^2x^5), x, n+1), x, n), n = 1..50); # G. C. Greubel, Oct 19 2019


MATHEMATICA

Rest[CoefficientList[Series[x^2*(2+3*x+2*x^33*x^6)/(1x^2x^5), {x, 0, 50}], x]] (* Harvey P. Dale, Oct 23 2011 *)


PROG

(PARI) my(x='x+O('x^50)); concat([0], Vec(x^2*(2+3*x+2*x^33*x^6)/(1x^2x^5))) \\ G. C. Greubel, Oct 19 2019
(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x^2*(2+3*x+2*x^33*x^6)/(1x^2x^5) )); // G. C. Greubel, Oct 19 2019
(Sage)
def A007387_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(x^2*(2+3*x+2*x^33*x^6)/(1x^2x^5)).list()
a=A007387_list(50); a[1:] # G. C. Greubel, Oct 19 2019


CROSSREFS

Cf. A001608, A007388, A007389.
Sequence in context: A007389 A007388 A057815 * A105222 A280503 A094757
Adjacent sequences: A007384 A007385 A007386 * A007388 A007389 A007390


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mira Bernstein


EXTENSIONS

More terms from Harvey P. Dale, Oct 23 2011


STATUS

approved



