STATUS
reviewed
approved
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Revision History for A253218
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Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
NAME
Number of nX3 n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
COMMENTS
Column 3 of A253223
FORMULA
Empirical: a(n) = 40*n^2 - 279*n + 497 for n>4.
Conjectures from Colin Barker, Dec 09 2018: (Start)
G.f.: x*(1 - 2*x + x^2 + 18*x^3 + 47*x^4 + 13*x^5 + 2*x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
EXAMPLE
Some solutions for n=4:
CROSSREFS
Column 3 of A253223.
STATUS
approved
editing
STATUS
editing
approved
LINKS
R. H. Hardin, <a href="/A253218/b253218.txt">Table of n, a(n) for n = 1..210</a>
NAME
allocated for R. H. Hardin
Number of nX3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value within 2 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down
DATA
1, 1, 1, 19, 102, 263, 504, 825, 1226, 1707, 2268, 2909, 3630, 4431, 5312, 6273, 7314, 8435, 9636, 10917, 12278, 13719, 15240, 16841, 18522, 20283, 22124, 24045, 26046, 28127, 30288, 32529, 34850, 37251, 39732, 42293, 44934, 47655, 50456, 53337, 56298
OFFSET
1,4
COMMENTS
Column 3 of A253223
FORMULA
Empirical: a(n) = 40*n^2 - 279*n + 497 for n>4
EXAMPLE
Some solutions for n=4
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1....0..0..1
..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..1..1....0..0..1
..0..0..1....0..1..1....0..1..1....1..1..1....1..1..1....1..1..1....0..0..1
..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
KEYWORD
allocated
nonn
AUTHOR
R. H. Hardin, Dec 29 2014
STATUS
approved
editing
NAME
allocated for R. H. Hardin
KEYWORD
allocated
STATUS
approved