A007382 Number of strict (-1)st-order maximal independent sets in path graph. (Formerly M2365)

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

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: A248825 A001641 A374712 * A127804 A027306 A239024

Adjacent sequences: A007379 A007380 A007381 * A007383 A007384 A007385

Keyword

nonn,easy

Author

N. J. A. Sloane, Mira Bernstein

Status

approved