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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. 1
0, 0, 0, 5, 24, 142, 840, 4919, 28704, 167344, 975408, 5685161, 33135624, 193128658, 1125636408, 6560689883, 38238502992, 222870328180, 1298983466208, 7571030469197, 44127199349112, 257192165625622, 1499025794404776 (list; graph; refs; listen; history; text; internal format)
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 A228067 A322208

Adjacent sequences:  A221785 A221786 A221787 * A221789 A221790 A221791

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 25 2013

STATUS

approved

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Last modified September 24 15:40 EDT 2021. Contains 347643 sequences. (Running on oeis4.)