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A214384 T(n,k)=Number of nXnXn triangular 0..k arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.

%I A214384 #6 Jul 22 2025 23:16:19
%S A214384 2,3,4,4,14,8,5,32,94,16,6,60,456,890,32,7,100,1506,11048,11700,64,8,
%T A214384 154,3976,74260,445024,211760,128,9,224,9044,350232,6981540,29456216,
%U A214384 5247716,256,10,312,18480,1305392,65905056,1232720402,3183854216,177440488,512
%N A214384 T(n,k)=Number of nXnXn triangular 0..k arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.
%C A214384 Table starts
%C A214384 ..2.....3......4.......5........6.........7..........8...........9..........10
%C A214384 ..4....14.....32......60......100.......154........224.........312.........420
%C A214384 ..8....94....456....1506.....3976......9044......18480.......34812.......61512
%C A214384 .16...890..11048...74260...350232...1305392....4107248....11363940....28412824
%C A214384 .32.11700.445024.6981540.65905056.444106514.2347567992.10319444960.39220393240
%H A214384 R. H. Hardin, <a href="/A214384/b214384.txt">Table of n, a(n) for n = 1..98</a>
%F A214384 Empirical: rows n=1..5 are polynomials of degree n(n+1)/2 in k
%e A214384 Some solutions for n=3 k=3
%e A214384 ....1......1......1......3......1......3......1......1......2......1......3
%e A214384 ...2.1....1.2....1.2....3.1....1.2....1.3....2.0....1.0....1.3....1.0....3.1
%e A214384 ..0.2.0..1.3.1..0.2.1..2.3.0..1.2.3..2.1.3..3.0.3..1.2.0..2.1.3..0.1.0..3.0.2
%Y A214384 Row 2 is A159920(n+1)
%K A214384 nonn,tabl
%O A214384 1,1
%A A214384 _R. H. Hardin_ Jul 14 2012