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A007382 Number of strict (-1)st-order maximal independent sets in path graph.
(Formerly M2365)
2
0, 0, 3, 4, 11, 16, 32, 49, 87, 137, 231, 369, 608, 978, 1595, 2574, 4179, 6754, 10944, 17699, 28655, 46355, 75023, 121379, 196416, 317796, 514227, 832024, 1346267 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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..29.

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

FORMULA

John W. Layman observes that if b(n) = 1+A007382(n) then b(n) = b(n-1) + 3b(n-2) - 2b(n-3) - 3b(n-4) + b(n-5) + b(n-6) for all 27 terms shown.

G.f.: x^3*(x^3+2x^2-x-3)/((1-x-x^2)*(1-x^2)^2).

a(n) = Sum_{i=1..floor((n-1)/2)} C(n-i+1, i). - Wesley Ivan Hurt, Sep 19 2017

MATHEMATICA

Table[Sum[Binomial[n - i + 1, i], {i, Floor[(n - 1)/2]}], {n, 30}] (* or *)

Rest@ Abs@ CoefficientList[Series[x^3*(x^3 + 2 x^2 - x - 3)/((1 - x - x^2) (1 - x^2)^2), {x, 0, 30}], x] (* Michael De Vlieger, Sep 19 2017 *)

CROSSREFS

Equals A054451(n+1) - 1.

Sequence in context: A266384 A248825 A001641 * A127804 A027306 A239024

Adjacent sequences:  A007379 A007380 A007381 * A007383 A007384 A007385

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)