STATUS
proposed
approved
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Revision History for A184034
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing all changes.
1/16 the number of (n+1) X 5 0..3 arrays with all 2 X 2 subblocks having the same four values.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
1/16 the number of (n+1)X5 X 5 0..3 arrays with all 2X2 2 X 2 subblocks having the same four values.
COMMENTS
Column 4 of A184039.
FORMULA
Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
Conjectures from Colin Barker, Apr 10 2018: (Start)
G.f.: x*(91 - 170*x - 185*x^2 + 340*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 76 for n even.
a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 76 for n odd.
(End)
EXAMPLE
Some solutions for 3X53 X 5:
CROSSREFS
Cf. A184039.
AUTHOR
R. H. Hardin , Jan 08 2011
STATUS
approved
editing
AUTHOR
_R. H. Hardin (rhhardin(AT)att.net) _ Jan 08 2011
STATUS
proposed
approved
LINKS
R. H. Hardin, <a href="/A184034/b184034.txt">Table of n, a(n) for n = 1..200</a>
NAME
allocated for Ron Hardin1/16 the number of (n+1)X5 0..3 arrays with all 2X2 subblocks having the same four values
DATA
91, 103, 124, 166, 244, 400, 700, 1300, 2476, 4828, 9484, 18796, 37324, 74380, 148300, 296140, 591436, 1182028, 2362444, 4723276, 9443404, 18883660, 37761100, 75515980, 151019596, 302026828, 604029004, 1208033356, 2416017484, 4831985740
OFFSET
1,1
COMMENTS
Column 4 of A184039
FORMULA
Empirical: a(n)=3*a(n-1)-6*a(n-3)+4*a(n-4)
EXAMPLE
Some solutions for 3X5
..3..1..0..1..3....2..3..3..3..3....2..1..2..0..2....1..1..3..2..1
..0..2..3..2..0....3..0..2..0..2....3..0..3..1..3....3..2..1..1..3
..3..1..0..1..3....2..3..3..3..3....2..1..2..0..2....1..1..3..2..1
KEYWORD
allocated
nonn
AUTHOR
R. H. Hardin (rhhardin(AT)att.net) Jan 08 2011
STATUS
approved
proposed
NAME
allocated for Ron Hardin
KEYWORD
allocated
STATUS
approved