A007380 Number of 5th-order maximal independent sets in path graph. (Formerly M0132)

1, 2, 1, 3, 1, 4, 2, 5, 4, 6, 7, 7, 11, 9, 16, 13, 22, 20, 29, 31, 38, 47, 51, 69, 71, 98, 102, 136, 149, 187, 218, 258, 316, 360, 452, 509, 639, 727, 897, 1043, 1257, 1495, 1766, 2134, 2493, 3031, 3536, 4288, 5031, 6054, 7165, 8547, 10196

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

Table of n, a(n) for n=1..53.

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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

Formula

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

a(n) = T(2, 7, n + 7) where T(a, b, n) = Sum_{a*x+b*y = n, x >= 0, y >= 0} binomial(x+y, y). - Sean A. Irvine, Jan 02 2018

Crossrefs

Sequence in context: A246582 A059499 A113322 * A369813 A319162 A029171

Adjacent sequences: A007377 A007378 A007379 * A007381 A007382 A007383

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Sean A. Irvine, Jan 02 2018

Status

approved