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A252979
Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.
1
3, 13, 33, 68, 1247, 8487, 27905, 62977, 114433, 182273, 266497, 367105, 484097, 617473, 767233, 933377, 1115905, 1314817, 1530113, 1761793, 2009857, 2274305, 2555137, 2852353, 3165953, 3495937, 3842305, 4205057, 4584193, 4979713, 5391617
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 8192*n^2 - 87808*n + 241153 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x*(3 + 4*x + 3*x^2 + 5*x^3 + 1129*x^4 + 4917*x^5 + 6117*x^6 + 3476*x^7 + 730*x^8) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
(End)
EXAMPLE
Some solutions for n=4:
..0..0..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..0
..0..1..1..1....0..0..1..1....0..0..0..0....0..1..1..1....0..1..1..1
..0..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1
..1..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1
CROSSREFS
Column 4 of A252983.
Sequence in context: A147137 A146230 A166805 * A332366 A033943 A026084
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 25 2014
STATUS
approved