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Number of 5th-order maximal independent sets in path graph.
(Formerly M0132)
22

%I M0132 #22 Feb 02 2021 21:59:49

%S 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,

%T 136,149,187,218,258,316,360,452,509,639,727,897,1043,1257,1495,1766,

%U 2134,2493,3031,3536,4288,5031,6054,7165,8547,10196

%N Number of 5th-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>

%H R. Yanco and A. Bagchi, <a href="/A007380/a007380_1.pdf">K-th order maximal independent sets in path and cycle graphs</a>, Unpublished manuscript, 1994. (Annotated scanned copy)

%F 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

%F 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

%K nonn

%O 1,2

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

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