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%I #8 Dec 06 2018 10:10:12
%S 4,17,63,187,468,1032,2067,3840,6716,11179,17855,27537,41212,60090,
%T 85635,119598,164052,221429,294559,386711,501636,643612,817491,
%U 1028748,1283532,1588719,1951967,2381773,2887532,3479598,4169347,4969242,5892900,6955161
%N 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.
%H R. H. Hardin, <a href="/A252815/b252815.txt">Table of n, a(n) for n = 1..210</a>
%F 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.
%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)
%F G.f.: x*(4 - 11*x + 28*x^2 - 37*x^3 + 27*x^4 - 11*x^5 + 2*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..0..1....0..0..0....0..1..1....0..0..1....0..1..2....0..1..2....0..1..1
%e ..0..0..1....1..1..1....1..2..2....1..1..2....1..2..2....1..2..3....0..1..1
%e ..1..1..2....1..1..2....2..2..3....1..2..2....2..3..3....1..2..3....1..1..2
%e ..1..2..3....2..2..3....2..3..4....1..2..3....2..3..3....1..2..3....2..2..3
%Y Column 3 of A252820.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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