A007392 Number of strict 3rd-order maximal independent sets in cycle graph. (Formerly M3727)

0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 12, 0, 21, 5, 32, 17, 45, 38, 65, 70, 99, 115, 156, 180, 247, 279, 385, 435, 590, 682, 896, 1067, 1360, 1657, 2073, 2553, 3173, 3913, 4865, 5986, 7455, 9159, 11407, 14024, 17434, 21479, 26636, 32886, 40705, 50320

Offset

1,10

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"K-th order maximal independent sets in path and cycle graphs", Journal of Graph Theory, submitted, 1994, apparently unpublished.

Links

Table of n, a(n) for n=1..51.

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

Formula

Conjecture: a(n) = 3*a(n-2) - 3*a(n-4) + a(n-5) + a(n-6) - 2*a(n-7) + a(n-9) with g.f. x^10*(-5+3*x^2)/((x^5+x^2-1)*(x-1)^2*(1+x)^2). - R. J. Mathar, Oct 30 2009

a(n) = A007387(n) - b(n) where b(1) = 0, b(2*n+1) = 2*n+1, b(2*n) = 2. - Sean A. Irvine, Jan 02 2018

Crossrefs

Cf. A007387.

Sequence in context: A340950 A156550 A208477 * A292105 A052401 A222946

Adjacent sequences: A007389 A007390 A007391 * A007393 A007394 A007395

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Sean A. Irvine, Jan 02 2018

Status

approved