A007386 Number of strict 7th-order maximal independent sets in path graph.
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 6, 0, 10, 0, 15, 1, 21, 4, 28, 10, 36, 20, 45, 35, 56, 56, 71, 84, 93, 120, 126, 165, 175, 221, 246, 292, 346, 385, 483, 511, 666, 686, 906, 932, 1218, 1278, 1624, 1761, 2157, 2427, 2866, 3333, 3822, 4551
Offset: 1
Keywords
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A. Bagchi, "K-th order maximal independent sets in path and cycle graphs", J. Graph Theory, submitted, 1994, apparently unpublished.
Links
Crossrefs
Cf. A007381.
Formula
Apparently, g.f. = -x^9/((x^9+x^2-1)*(x-1)^2*(1+x)^2) with recurrence a(n)= 3*a(n-2) - 3*a(n-4) + a(n-6) + a(n-9) - 2*a(n-11) + a(n-13). - R. J. Mathar, Oct 30 2009
a(n) = A007381(n) - 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