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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 (list; graph; refs; listen; history; text; internal format)
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, ``K-th 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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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^2-1). - 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

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Last modified July 22 21:28 EDT 2019. Contains 325227 sequences. (Running on oeis4.)