The On-Line Encyclopedia of Integer Sequences (OEIS)

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A304770

Number of n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.
(history; published version)

#6 by Wesley Ivan Hurt at Thu Dec 28 23:21:20 EST 2023

STATUS

editing

approved

#5 by Wesley Ivan Hurt at Thu Dec 28 23:21:07 EST 2023

NAME

Number of nX3 n X 3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.

FORMULA

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) for n>8.

STATUS

approved

editing

#4 by R. H. Hardin at Fri May 18 08:11:37 EDT 2018

STATUS

editing

approved

#3 by R. H. Hardin at Fri May 18 08:11:34 EDT 2018

LINKS

R. H. Hardin, <a href="/A304770/b304770.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Fri May 18 08:11:18 EDT 2018

NAME

allocated for R. H. Hardin

Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.

DATA

4, 21, 27, 67, 139, 303, 685, 1511, 3316, 7349, 16265, 35899, 79332, 175408, 387618, 856555, 1893162, 4184055, 9246710, 20435743, 45164387, 99815208, 220596189, 487529334, 1077464178, 2381248108, 5262677458, 11630780579, 25704601383

OFFSET

1,1

COMMENTS

Column 3 of A304775.

FORMULA

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) for n>8

EXAMPLE

Some solutions for n=5

..0..1..1. .0..0..1. .0..1..0. .0..0..1. .0..1..1. .0..1..1. .0..0..0

..0..1..1. .0..0..0. .1..1..1. .0..0..0. .1..1..1. .0..0..1. .0..1..0

..1..0..1. .0..0..0. .1..1..1. .0..0..0. .1..1..1. .0..0..0. .0..0..1

..1..1..1. .0..0..0. .1..1..1. .1..0..0. .0..1..1. .0..0..0. .0..1..0

..1..1..1. .1..1..1. .1..1..0. .1..1..0. .0..0..1. .1..0..1. .0..0..0

CROSSREFS

Cf. A304775.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, May 18 2018

STATUS

approved

editing

#1 by R. H. Hardin at Fri May 18 08:10:05 EDT 2018

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved