A007381 7th-order maximal independent sets in path graph.

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

Examples

			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 + ...
		

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• R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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

Extensions

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

More terms from Sean A. Irvine, Jan 02 2018