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Number of strict 3rd-order maximal independent sets in path graph.
(Formerly M2201)
0

%I M2201 #17 Jan 02 2018 17:08:42

%S 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,

%T 221,295,346,449,539,684,834,1045,1283,1600,1967,2451,3012,3752,4612,

%U 5738,7063,8770,10815,13403,16553,20488,25323,31326,38726

%N Number of strict 3rd-order maximal independent sets in path graph.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D R. Yanco and A. Bagchi, ``K-th order maximal independent sets in path and cycle graphs,'' J. Graph Theory, submitted, 1994.

%H R. Yanco, <a href="/A007380/a007380.pdf">Letter and Email to N. J. A. Sloane, 1994</a>

%F 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]

%F 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

%Y Cf. A001687.

%K nonn

%O 1,7

%A _N. J. A. Sloane_, _Mira Bernstein_

%E More terms from _Sean A. Irvine_, Jan 02 2018