A007389 -id:A007389 - cp's OEIS frontend

A007387 Number of 3rd-order maximal independent sets in cycle graph.

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

Offset: 1

N. J. A. Sloane, Mira Bernstein

nonn

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.

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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

Cf. A001608, A007388, A007389.

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

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

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 *)

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

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

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

More terms from Harvey P. Dale, Oct 23 2011

A007388 5th-order maximal independent sets in cycle graph.

Original entry on oeis.org

0, 2, 3, 2, 5, 2, 7, 2, 9, 2, 11, 2, 13, 9, 15, 18, 17, 29, 19, 42, 28, 57, 46, 74, 75, 93, 117, 121, 174, 167, 248, 242, 341, 359, 462, 533, 629, 781, 871, 1122, 1230, 1584, 1763, 2213, 2544, 3084, 3666, 4314, 5250, 6077, 7463, 8621, 10547

Offset: 1

N. J. A. Sloane, Mira Bernstein

nonn

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, apparently unpublished.

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)

Cf. A001608, A007387, A007389.

Empirical g.f.: x^2*(5*x^10+3*x^8-2*x^5-2*x^3-3*x-2) / (x^7+x^2-1). - Colin Barker, Mar 29 2014
For n >= 13: a(n) = a(n-2) + a(n-7). - Sean A. Irvine, Jan 02 2018
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), g = 7, n >= g and n an odd integer. - Richard Turk, Oct 14 2019

Typo in data (242 was inadvertently repeated) fixed by Colin Barker, Mar 29 2014

More terms from Sean A. Irvine, Jan 02 2018

A007394 Number of strict 7th-order maximal independent sets in cycle graph.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 20, 0, 33, 0, 48, 0, 65, 9, 84, 29, 105, 62, 128, 110, 153, 175, 189, 259, 247, 364, 340, 492, 483, 645, 693, 834, 989, 1081, 1392, 1421, 1925, 1904, 2613, 2597, 3492, 3586, 4620, 4978, 6090

Offset: 1

N. J. A. Sloane, Mira Bernstein

nonn

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.

R. Yanco, Letter and Email to N. J. A. Sloane, 1994

Cf. A007389.

Empirical g.f.: x^18*(7*x^2-9) / ((x-1)^2*(x+1)^2*(x^9+x^2-1)). - Colin Barker, Mar 29 2014

a(n) = A007389(n) - b(n) where b(1) = 0, b(2*n+1) = 2*n+1, b(2*n) = 2. - Sean A. Irvine, Jan 02 2018

More terms from Sean A. Irvine, Jan 02 2018

cp's OEIS Frontend

A007387 Number of 3rd-order maximal independent sets in cycle graph.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

Extensions

A007388 5th-order maximal independent sets in cycle graph.

Views

Author

Keywords

References

Links

Crossrefs

Formula

Extensions

A007394 Number of strict 7th-order maximal independent sets in cycle graph.

Views

Author

Keywords

References

Links

Crossrefs

Formula

Extensions