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A214542 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.

%I A214542 #6 Jul 22 2025 23:17:41
%S A214542 2,93,344,1181,3198,7801,16752,33605,62766,111653,189264,309453,
%T A214542 488806,751289,1124676,1647473,2364174,3333765,4623132,6319045,
%U A214542 8519174,11346717,14938900,19465789,25115826,32118473,40725436,51239465,63991794,79374993
%N A214542 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 A214542 Row 4 of A214540
%H A214542 R. H. Hardin, <a href="/A214542/b214542.txt">Table of n, a(n) for n = 1..130</a>
%F A214542 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 A214542 Some solutions for n=4
%e A214542 .....3........3........2........1........2........2........2........1
%e A214542 ....2.4......3.3......3.1......2.0......2.2......2.2......1.3......2.0
%e A214542 ...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 A214542 ..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 A214542 nonn
%O A214542 1,1
%A A214542 _R. H. Hardin_ Jul 20 2012