A231882 Number of maximal 2-independent sets in the planar 3 X n grid graph.

0, 3, 4, 11, 17, 36, 69, 133, 254, 499, 959, 1852, 3589, 6943, 13410, 25951, 50197, 97050, 187699, 363047, 702066, 1357755, 2625947, 5078438, 9821417, 18994465, 36734648, 71043261, 137395463, 265718350, 513889567, 993844901, 1922062694, 3717202293, 7188941039

Offset: 0

Author

N. J. A. Sloane, Nov 17 2013

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• R. Euler, P. Oleksik, Z. Skupien, Counting Maximal Distance-Independent Sets in Grid Graphs, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see also.
• Index entries for linear recurrences with constant coefficients, signature (1,0,3,1,0,1,-2,0,-1).

Crossrefs

Cf. A197054, A197049.

Programs

Mathematica

LinearRecurrence[{1,0,3,1,0,1,-2,0,-1},{0,3,4,11,17,36,69,133,254,499},40] (* Harvey P. Dale, Oct 05 2017 *)

Formula

Euler et al. give an explicit g.f. and recurrence.

G.f.: x*(3 + x + 7*x^2 - 3*x^3 + 4*x^4 - 4*x^5 - x^6 - 2*x^7 - x^8) / ((1 + x)*(1 - 2*x + 2*x^2 - 5*x^3 + 4*x^4 - 4*x^5 + 3*x^6 - x^7 + x^8)). - Colin Barker, Oct 03 2017

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jun 10 2017