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A252815 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down. 1
4, 17, 63, 187, 468, 1032, 2067, 3840, 6716, 11179, 17855, 27537, 41212, 60090, 85635, 119598, 164052, 221429, 294559, 386711, 501636, 643612, 817491, 1028748, 1283532, 1588719, 1951967, 2381773, 2887532, 3479598, 4169347, 4969242, 5892900, 6955161 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (1/2)*n^3 + (439/360)*n^2 - (1/20)*n + 2.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(4 - 11*x + 28*x^2 - 37*x^3 + 27*x^4 - 11*x^5 + 2*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Some solutions for n=4:
..0..0..1....0..0..0....0..1..1....0..0..1....0..1..2....0..1..2....0..1..1
..0..0..1....1..1..1....1..2..2....1..1..2....1..2..2....1..2..3....0..1..1
..1..1..2....1..1..2....2..2..3....1..2..2....2..3..3....1..2..3....1..1..2
..1..2..3....2..2..3....2..3..4....1..2..3....2..3..3....1..2..3....2..2..3
CROSSREFS
Column 3 of A252820.
Sequence in context: A202752 A286210 A339286 * A362593 A191272 A122231
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved

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Last modified July 20 07:46 EDT 2024. Contains 374442 sequences. (Running on oeis4.)