A221591 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less.

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

Offset

1,2

Comments

Column 2 of A221596.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (2,2,1).

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

Adjacent sequences: A221588 A221589 A221590 * A221592 A221593 A221594

Keyword

nonn,easy

Author

R. H. Hardin, Jan 20 2013

Status

approved