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A214908 Number of 4X4X4 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.

%I A214908 #6 Jul 22 2025 23:20:07
%S A214908 2,14,50,182,458,1184,2490,5213,9722,17864,30284,51088,80840,127040,
%T A214908 191162,285357,410940,589294,820180,1136378,1538406,2072864,2738172,
%U A214908 3606249,4667108,6021672,7659902,9714004,12163526,15197912,18774496
%N A214908 Number of 4X4X4 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value.
%C A214908 Row 4 of A214906
%H A214908 R. H. Hardin, <a href="/A214908/b214908.txt">Table of n, a(n) for n = 1..210</a>
%F A214908 Empirical: a(n) = a(n-4) +2*a(n-6) +2*a(n-8) +2*a(n-9) -2*a(n-10) -2*a(n-12) -2*a(n-13) -4*a(n-14) -4*a(n-15) -a(n-16) -4*a(n-17) +a(n-18) +4*a(n-19) +a(n-20) +4*a(n-21) +5*a(n-22) +8*a(n-23) +3*a(n-24) +2*a(n-25) +4*a(n-26) -4*a(n-27) -3*a(n-28) -2*a(n-29) -6*a(n-30) -8*a(n-31) -6*a(n-32) -2*a(n-33) -3*a(n-34) -4*a(n-35) +4*a(n-36) +2*a(n-37) +3*a(n-38) +8*a(n-39) +5*a(n-40) +4*a(n-41) +a(n-42) +4*a(n-43) +a(n-44) -4*a(n-45) -a(n-46) -4*a(n-47) -4*a(n-48) -2*a(n-49) -2*a(n-50) -2*a(n-52) +2*a(n-53) +2*a(n-54) +2*a(n-56) +a(n-58) -a(n-62)
%e A214908 Some solutions for n=4
%e A214908 .....2........2........2........2........3........2........2........2
%e A214908 ....2.2......1.3......1.3......2.2......2.4......1.3......1.3......0.4
%e A214908 ...1.1.4....1.2.3....0.3.3....2.2.2....2.3.4....1.2.3....0.3.3....0.2.4
%e A214908 ..1.1.3.3..1.1.3.3..0.1.3.4..0.1.3.4..1.3.4.4..0.2.2.4..2.2.2.2..1.2.2.3
%K A214908 nonn
%O A214908 1,1
%A A214908 _R. H. Hardin_ Jul 29 2012