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%I #4 Jul 20 2012 11:49:20
%S 2,93,344,1181,3198,7801,16752,33605,62766,111653,189264,309453,
%T 488806,751289,1124676,1647473,2364174,3333765,4623132,6319045,
%U 8519174,11346717,14938900,19465789,25115826,32118473,40725436,51239465,63991794,79374993
%N Number of 4X4X4 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value
%C Row 4 of A214540
%H R. H. Hardin, <a href="/A214542/b214542.txt">Table of n, a(n) for n = 1..130</a>
%F Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -3*a(n-5) -2*a(n-6) -2*a(n-7) +4*a(n-8) +3*a(n-9) +2*a(n-10) -a(n-11) -3*a(n-12) -a(n-13) -a(n-14) +4*a(n-15) -a(n-16) -a(n-17) -3*a(n-18) -a(n-19) +2*a(n-20) +3*a(n-21) +4*a(n-22) -2*a(n-23) -2*a(n-24) -3*a(n-25) +a(n-27) +a(n-28) +a(n-29) -a(n-30)
%e Some solutions for n=4
%e .....3........3........2........1........2........2........2........1
%e ....2.4......3.3......3.1......2.0......2.2......2.2......1.3......2.0
%e ...2.4.3....2.3.4....3.2.1....1.2.0....2.2.2....1.4.1....1.4.1....2.1.0
%e ..3.2.4.3..2.3.3.4..0.3.1.4..0.2.2.0..1.2.3.2..1.4.1.2..1.4.2.1..3.1.0.0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jul 20 2012
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