This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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Table of n, a(n) for n = 1..1000 R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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:=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. = 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 EXTENSIONS More terms from Harvey P. Dale, Oct 23 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)