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%I A007381 M0130 #29 Jan 31 2021 20:44:12
%S A007381 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,
%T A007381 72,100,94,137,127,183,176,240,247,312,347,406,484,533,667,709,907,
%U A007381 956,1219,1303,1625,1787,2158,2454,2867,3361,3823,4580
%N A007381 7th-order maximal independent sets in path graph.
%D A007381 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007381 R. Yanco and A. Bagchi, "K-th order maximal independent sets in path and cycle graphs," J. Graph Theory, submitted, 1994.
%H A007381 R. Yanco, <a href="/A007380/a007380.pdf">Letter and Email to N. J. A. Sloane, 1994</a>
%H A007381 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, Unpublished manuscript, 1994.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 A007381 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
%F A007381 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
%e A007381 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 + ...
%K A007381 nonn
%O A007381 1,2
%A A007381 _N. J. A. Sloane_, _Mira Bernstein_
%E A007381 a(22) corrected by _Colin Barker_, Mar 29 2014
%E A007381 More terms from _Sean A. Irvine_, Jan 02 2018

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