

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
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OFFSET

1,2


COMMENTS



LINKS



FORMULA

a(n) = 2*a(n1) +2*a(n2) +a(n3) 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



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



