OFFSET
0,2
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 (0,3,4,4,0,-9,-3).
FORMULA
Euler et al. give an explicit g.f. and recurrence.
From Colin Barker, Oct 04 2017: (Start)
G.f.: 4*x*(1 + x)*(1 + 2*x^2 - x^3 - 2*x^4 - x^5) / (1 - 3*x^2 - 4*x^3 - 4*x^4 + 9*x^6 + 3*x^7).
a(n) = 3*a(n-2) + 4*a(n-3) + 4*a(n-4) - 9*a(n-6) - 3*a(n-7) for n>7.
(End)
MATHEMATICA
Join[{0}, LinearRecurrence[{0, 3, 4, 4, 0, -9, -3}, {4, 4, 20, 32, 80, 180, 408}, 31]] (* Jean-François Alcover, Nov 01 2017 *)
PROG
(PARI) concat(0, Vec(4*x*(1 + x)*(1 + 2*x^2 - x^3 - 2*x^4 - x^5) / (1 - 3*x^2 - 4*x^3 - 4*x^4 + 9*x^6 + 3*x^7) + O(x^40))) \\ Colin Barker, Oct 04 2017
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 17 2013
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jun 10 2017
STATUS
approved