

A007381


7th order maximal independent sets in path graph.
(Formerly M0130)


1



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
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OFFSET

1,2


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. Yanco and A. Bagchi, ``Kth order maximal independent sets in path and cycle graphs,'' J. Graph Theory, submitted, 1994.


LINKS

Table of n, a(n) for n=1..56.
R. Yanco, Letter and Email to N. J. A. Sloane, 1994
R. Yanco and A. Bagchi, Kth order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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^21).  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


EXAMPLE

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 + ...


CROSSREFS

Sequence in context: A194746 A198336 A290980 * A308059 A319698 A087114
Adjacent sequences: A007378 A007379 A007380 * A007382 A007383 A007384


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mira Bernstein


EXTENSIONS

a(22) corrected by Colin Barker, Mar 29 2014
More terms from Sean A. Irvine, Jan 02 2018


STATUS

approved



