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%I #8 Dec 06 2018 19:24:00
%S 2,6,18,53,142,339,729,1437,2638,4568,7536,11937,18266,27133,39279,
%T 55593,77130,105130,141038,186525,243510,314183,401029,506853,634806,
%U 788412,971596,1188713,1444578,1744497,2094299,2500369,2969682,3509838,4129098
%N Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.
%H R. H. Hardin, <a href="/A252822/b252822.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (5/144)*n^4 - (11/48)*n^3 + (527/360)*n^2 - (3/10)*n + 1.
%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)
%F G.f.: x*(2 - 8*x + 18*x^2 - 17*x^3 + 9*x^4 - 4*x^5 + x^6) / (1 - x)^7.
%F 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.
%F (End)
%e Some solutions for n=4:
%e ..0..1....0..0....0..0....0..1....0..0....0..0....0..0....0..1....0..0....0..0
%e ..0..1....0..0....0..0....0..1....0..1....1..1....1..1....1..2....1..1....1..1
%e ..0..1....0..1....1..1....0..1....1..1....2..2....1..1....2..2....1..2....1..1
%e ..1..1....1..2....1..2....0..1....1..1....2..2....2..2....3..3....2..2....1..1
%Y Column 2 of A252828.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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