A221788 Number of 3 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without 2-loops or left turns.

0, 0, 0, 5, 24, 142, 840, 4919, 28704, 167344, 975408, 5685161, 33135624, 193128658, 1125636408, 6560689883, 38238502992, 222870328180, 1298983466208, 7571030469197, 44127199349112, 257192165625622, 1499025794404776

Offset

1,4

Comments

Row 3 of A221787.

Links

R. H. Hardin, Table of n, a(n) for n = 1..85

Formula

Empirical: a(n) = 8*a(n-1) - 14*a(n-2) + 8*a(n-3) - a(n-4) for n>6.

Conjectures from Colin Barker, Aug 10 2018: (Start)

G.f.: x^4*(5 - 16*x + 20*x^2) / ((1 - x)^2*(1 - 6*x + x^2)).

a(n) = (408 + sqrt(2)*((10041-7100*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(10041+7100*sqrt(2))) - 72*(1+n)) / 32 for n>2.

(End)

Crossrefs

Cf. A221787.

Sequence in context: A286743 A232318 A201952 * A111766 A368534 A228067

Adjacent sequences: A221785 A221786 A221787 * A221789 A221790 A221791

Keyword

nonn

Author

R. H. Hardin, Jan 25 2013

Status

approved