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A214597 Number of 4X4X4 triangular 0..n arrays with every horizontal row having the same average value.

%I A214597 #10 Aug 21 2025 10:00:49
%S A214597 2,401,1862,10177,33352,103651,250042,589763,1199614,2377843,4299560,
%T A214597 7631589,12644114,20709813,32235854,49618485,73512984,107991735,
%U A214597 153683050,217344807,299596702,410511063,550861288,735611705,964611698
%N A214597 Number of 4X4X4 triangular 0..n arrays with every horizontal row having the same average value.
%H A214597 R. H. Hardin, <a href="/A214597/b214597.txt">Table of n, a(n) for n = 1..210</a>
%F A214597 Empirical: a(n) = -3*a(n-1) -4*a(n-2) +a(n-3) +15*a(n-4) +28*a(n-5) +22*a(n-6) -18*a(n-7) -74*a(n-8) -96*a(n-9) -42*a(n-10) +78*a(n-11) +177*a(n-12) +165*a(n-13) +24*a(n-14) -155*a(n-15) -234*a(n-16) -155*a(n-17) +24*a(n-18) +165*a(n-19) +177*a(n-20) +78*a(n-21) -42*a(n-22) -96*a(n-23) -74*a(n-24) -18*a(n-25) +22*a(n-26) +28*a(n-27) +15*a(n-28) +a(n-29) -4*a(n-30) -3*a(n-31) -a(n-32)
%e A214597 Some solutions for n=4
%e A214597 .....2........2........2........2........2........2........1........2
%e A214597 ....3.1......2.2......1.3......2.2......4.0......1.3......2.0......4.0
%e A214597 ...2.2.2....1.2.3....3.2.1....0.2.4....1.1.4....4.2.0....0.3.0....4.2.0
%e A214597 ..2.3.3.0..3.3.2.0..3.3.1.1..3.0.4.1..2.3.2.1..0.4.0.4..1.0.3.0..3.4.0.1
%Y A214597 Row 4 of A214595.
%K A214597 nonn,changed
%O A214597 1,1
%A A214597 _R. H. Hardin_, Jul 22 2012