A007381 7th-order maximal independent sets in path graph. (Formerly M0130)

1, 2, 1, 3, 1, 4, 1, 5, 2, 6, 4, 7, 7, 8, 11, 9, 16, 11, 22, 15, 29, 22, 37, 33, 46, 49, 57, 71, 72, 100, 94, 137, 127, 183, 176, 240, 247, 312, 347, 406, 484, 533, 667, 709, 907, 956, 1219, 1303, 1625, 1787, 2158, 2454, 2867, 3361, 3823, 4580

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..56.

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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

Empirical g.f.: -x*(x^8+x^7+x^5+x^3+2*x+1) / (x^9+x^2-1). - Colin Barker, Mar 29 2014

a(n) = T(2, 9, n + 9) 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

Example

G.f. = x + 2*x^2 + x^3 + 3*x^4 + x^5 + 4*x^6 + 5*x^7 + 2*x^8 + 6*x^9 + ...

Crossrefs

Sequence in context: A330747 A337785 A290980 * A366877 A337377 A308059

Adjacent sequences: A007378 A007379 A007380 * A007382 A007383 A007384

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

a(22) corrected by Colin Barker, Mar 29 2014

More terms from Sean A. Irvine, Jan 02 2018

Status

approved