A007390 Number of strict (-1)st-order maximal independent sets in cycle graph. (Formerly M3257)

0, 0, 0, 4, 5, 15, 21, 44, 66, 120, 187, 319, 507, 840, 1348, 2204, 3553, 5775, 9329, 15124, 24454, 39600, 64055, 103679, 167735, 271440, 439176, 710644, 1149821, 1860495, 3010317, 4870844, 7881162, 12752040, 20633203, 33385279, 54018483

Offset

1,4

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..37.

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

Formula

a(n) = A000204(n) - b(n) where b(1) = 1, b(2*n+1) = 2*n+2, b(2*n) = 3. - Sean A. Irvine, Jan 02 2018

Conjectures from Colin Barker, Jun 14 2019: (Start)

G.f.: x^4*(4 + x - 2*x^2 - x^3) / ((1 - x)^2*(1 + x)^2*(1 - x - x^2)).

a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 3*a(n-4) + a(n-5) + a(n-6) for n>7.

(End)

Crossrefs

Sequence in context: A002509 A230983 A100234 * A037955 A225121 A267991

Adjacent sequences: A007387 A007388 A007389 * A007391 A007392 A007393

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

a(18) corrected and more terms from Sean A. Irvine, Jan 02 2018

Status

approved