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A295913
Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.
2
5, 13, 39, 115, 337, 993, 2919, 8587, 25257, 74289, 218511, 642715, 1890449, 5560465, 16355255, 48106475, 141497817, 416194129, 1224171199, 3600711835, 10590941633, 31151630513, 91627743527, 269508954923, 792719257161, 2331662118065
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OFFSET
1,1
COMMENTS
a(n) is the number of ways to tile a 4 X (n + 1) grid with 1 X 1, 2 X 2 and 3 X 3 tiles. -
Kiran Ananthpur Bacche
, Sep 09 2025
LINKS
R. H. Hardin,
Table of n, a(n) for n = 1..210
FORMULA
Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-4).
Empirical g.f.: x*(5 + 3*x - 2*x^2 - 2*x^3) / (1 - 2*x - 3*x^2 + 2*x^4). -
Colin Barker
, Feb 22 2019
EXAMPLE
Some solutions for n=7:
..0..0..1. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1
..0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..0..0. .1..0..1. .0..1..1
..0..1..0. .0..0..0. .0..1..1. .1..0..1. .0..1..1. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .1..0..1
..0..0..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0. .0..0..0
..0..0..0. .1..1..0. .0..0..0. .1..0..0. .1..0..0. .0..0..0. .0..0..0
..1..0..0. .0..0..0. .0..0..1. .0..0..1. .0..0..1. .0..0..1. .0..0..0
CROSSREFS
Column 3 of
A295918
.
Sequence in context:
A360797
A080143
A077919
*
A272225
A272585
A026069
Adjacent sequences:
A295910
A295911
A295912
*
A295914
A295915
A295916
KEYWORD
nonn
AUTHOR
R. H. Hardin
, Nov 29 2017
STATUS
approved
