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 A007387 Number of 3rd-order maximal independent sets in cycle graph. (Formerly M0426) 5

%I M0426

%S 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,

%T 249,306,387,464,592,713,898,1100,1362,1692,2075,2590,3175,3952,4867,

%U 6027,7457,9202,11409,14069,17436,21526,26638,32935,40707,50371,62233

%N Number of 3rd-order maximal independent sets in cycle graph.

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

%D R. Yanco and A. Bagchi, "K-th order maximal independent sets in path and cycle graphs," J. Graph Theory, submitted, 1994.

%H Harvey P. Dale, <a href="/A007387/b007387.txt">Table of n, a(n) for n = 1..1000</a>

%H R. Yanco, <a href="/A007380/a007380.pdf">Letter and Email to N. J. A. Sloane, 1994</a>

%H R. Yanco and A. Bagchi, <a href="/A007380/a007380_1.pdf">K-th order maximal independent sets in path and cycle graphs</a>, Unpublished manuscript, 1994. (Annotated scanned copy)

%F 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

%F G.f.: x^2*(2 + 3*x + 2*x^3 - 3*x^6)/(1 - x^2 - x^5). - _R. J. Mathar_, Oct 30 2009

%F 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

%p 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

%t 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 *)

%o (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

%o (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

%o (Sage)

%o def A007387_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P(x^2*(2+3*x+2*x^3-3*x^6)/(1-x^2-x^5)).list()

%o a=A007387_list(50); a[1:] # _G. C. Greubel_, Oct 19 2019

%Y Cf. A001608, A007388, A007389.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_

%E More terms from _Harvey P. Dale_, Oct 23 2011

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Last modified July 30 06:21 EDT 2021. Contains 346348 sequences. (Running on oeis4.)