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A007384 Number of strict 3rd-order maximal independent sets in path graph.
(Formerly M2201)
0
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, 221, 295, 346, 449, 539, 684, 834, 1045, 1283, 1600, 1967, 2451, 3012, 3752, 4612, 5738, 7063, 8770, 10815, 13403, 16553, 20488, 25323, 31326, 38726 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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..50.

R. Yanco, Letter and Email to N. J. A. Sloane, 1994

FORMULA

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]

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

CROSSREFS

Cf. A001687.

Sequence in context: A280585 A197807 A111074 * A290108 A334950 A171419

Adjacent sequences:  A007381 A007382 A007383 * A007385 A007386 A007387

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Sean A. Irvine, Jan 02 2018

STATUS

approved

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Last modified June 20 03:05 EDT 2021. Contains 345157 sequences. (Running on oeis4.)