A007384 Number of strict 3rd-order maximal independent sets in path graph. (Formerly M2201)

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

1,7

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

Table of n, a(n) for n=1..50.

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^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

Crossrefs

Cf. A001687.

Sequence in context: A359218 A197807 A111074 * A290108 A334950 A171419

Adjacent sequences: A007381 A007382 A007383 * A007385 A007386 A007387

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Sean A. Irvine, Jan 02 2018

Status

approved