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A214352 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.

%I A214352 #6 Jul 22 2025 23:15:01
%S A214352 2,3,6,4,17,26,5,36,169,160,6,65,660,2853,1386,7,106,1951,23554,80573,
%T A214352 16814,8,161,4822,127813,1602092,3778867,284724,9,232,10507,529006,
%U A214352 17790765,205613460,293207907,6715224,10,321,20840,1807653,135538054
%N A214352 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.
%C A214352 Table starts
%C A214352 ....2.....3.......4........5.........6.........7..........8...........9
%C A214352 ....6....17......36.......65.......106.......161........232.........321
%C A214352 ...26...169.....660.....1951......4822.....10507......20840.......38421
%C A214352 ..160..2853...23554...127813....529006...1807653....5349708....14150061
%C A214352 .1386.80573.1602092.17790765.135538054.790197579.3766437036.15329961031
%H A214352 R. H. Hardin, <a href="/A214352/b214352.txt">Table of n, a(n) for n = 1..99</a>
%F A214352 Empirical: rows n=1..5 are polynomials of degree n(n+1)/2 in k
%e A214352 Some solutions for n=3 k=3
%e A214352 ....0......0......1......1......2......2......2......2......2......3......3
%e A214352 ...0.1....3.0....1.1....0.2....2.1....1.2....3.1....0.2....2.0....3.3....3.2
%e A214352 ..2.0.3..3.1.0..0.3.0..0.3.2..3.0.2..1.2.0..3.0.2..3.0.2..2.3.0..1.3.1..3.2.3
%Y A214352 Column 1 is 2*A183278
%Y A214352 Row 2 is A084990(n+1)
%K A214352 nonn,tabl
%O A214352 1,1
%A A214352 _R. H. Hardin_ Jul 13 2012