

A268769


Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.


1



12, 32, 112, 446, 1524, 5214, 17000, 54822, 173244, 541910, 1676448, 5146030, 15683076, 47518926, 143238872, 429867830, 1285009740, 3828046534, 11368576272, 33669165246, 99465517716, 293175780030, 862355454792, 2531766659654
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OFFSET

1,1


LINKS

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


FORMULA

Empirical: a(n) = 4*a(n1) + 2*a(n2)  16*a(n3)  a(n4) + 12*a(n5)  4*a(n6) for n>8.
Empirical g.f.: 2*x*(6  8*x  20*x^2 + 63*x^3 + 20*x^4  47*x^5 + 4*x^6 + 4*x^7) / (1  2*x  3*x^2 + 2*x^3)^2.  Colin Barker, Jan 15 2019


EXAMPLE

Some solutions for n=4:
..1..0..0. .1..0..0. .0..0..0. .1..2..1. .1..1..0. .2..2..2. .1..2..1
..0..0..0. .1..0..0. .1..1..0. .1..2..2. .0..0..0. .1..2..2. .1..2..2
..1..0..1. .0..0..0. .0..0..0. .2..2..1. .0..0..0. .2..2..1. .2..2..2
..0..0..1. .1..0..0. .1..0..0. .1..2..2. .1..0..1. .2..1..2. .1..2..2


CROSSREFS

Column 3 of A268774.
Sequence in context: A143238 A102091 A303079 * A045669 A045660 A192213
Adjacent sequences: A268766 A268767 A268768 * A268770 A268771 A268772


KEYWORD

nonn


AUTHOR

R. H. Hardin, Feb 13 2016


STATUS

approved



