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A007387 Number of 3rd-order 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 (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).

R. Yanco and A. Bagchi, "K-th 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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy)

FORMULA

For n >= 9: a(n) = a(n-2) + a(n-5) 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((n-g)/(2*g))} (2*n/(n-2*(g-2)*j-(g-2))) * Hypergeometric2F1([-(n-2g*j-g)/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^3-3*x^6)/(1-x^2-x^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^3-3*x^6)/(1-x^2-x^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^3-3*x^6)/(1-x^2-x^5))) \\ G. C. Greubel, Oct 19 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x^2*(2+3*x+2*x^3-3*x^6)/(1-x^2-x^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^3-3*x^6)/(1-x^2-x^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

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Last modified June 12 22:34 EDT 2021. Contains 344974 sequences. (Running on oeis4.)