A007384 Number of strict 3rd-order maximal independent sets in path graph.

0, 0, 0, 0, 1, 0, 3, 0, 6, 1, 10, 4, 15, 10, 22, 20, 33, 35, 51, 57, 80, 90, 125, 141, 193, 221, 295, 346, 449, 539, 684, 834, 1045, 1283, 1600, 1967, 2451, 3012, 3752, 4612, 5738, 7063, 8770, 10815, 13403, 16553, 20488, 25323, 31326, 38726

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

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

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

Crossrefs

Cf. A001687.

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^5/((x^5+x^2-1)*(x-1)^2*(1+x)^2). [From R. J. Mathar, Oct 30 2009]

a(n) = A001687(n + 6) - b(n) where b(2*n+1) = 1 and b(2*n) = n+1. - Sean A. Irvine, Jan 02 2018

Extensions

More terms from Sean A. Irvine, Jan 02 2018