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A221591 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less. 1
0, 7, 17, 49, 139, 393, 1113, 3151, 8921, 25257, 71507, 202449, 573169, 1622743, 4594273, 13007201, 36825691, 104260057, 295178697, 835703199, 2366023849, 6698632793, 18965016483, 53693322401, 152015310561, 430382282407, 1218488508337, 3449756892049 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 2 of A221596.
LINKS
Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.
FORMULA
a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) for n>4.
G.f.: x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3). - Colin Barker, Jan 31 2017
EXAMPLE
Some solutions for n=6
..2....1....1....0....1....1....0....1....1....2....2....2....1....1....2....1
..2....1....2....0....2....0....1....1....0....2....2....1....1....1....1....1
..2....2....1....1....2....2....1....0....0....0....0....2....1....0....2....1
..1....2....0....0....2....1....0....1....2....1....1....2....0....2....0....2
..0....1....1....0....0....2....2....0....2....0....0....1....1....1....1....1
..0....2....2....1....0....2....1....0....1....0....1....2....1....1....0....2
PROG
(PARI) concat(0, Vec(x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + O(x^30))) \\ Colin Barker, Jan 31 2017
CROSSREFS
Sequence in context: A110097 A179262 A018672 * A045821 A262754 A115914
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved

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Last modified May 23 18:59 EDT 2024. Contains 372765 sequences. (Running on oeis4.)