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A195805 T(n,k)=Number of triangular nXnXn 0..k arrays with all rows and diagonals having the same length having the same sum, with corners zero.

%I A195805 #6 Jul 22 2025 12:47:13
%S A195805 1,1,1,1,1,2,1,1,3,8,1,1,4,27,16,1,1,5,64,105,64,1,1,6,125,496,1695,
%T A195805 1184,1,1,7,216,1759,24928,284427,5300,1,1,8,343,5052,213319,17528896,
%U A195805 11606931,130324,1,1,9,512,12469,1274808
%N A195805 T(n,k)=Number of triangular nXnXn 0..k arrays with all rows and diagonals having the same length having the same sum, with corners zero.
%C A195805 Table starts
%C A195805 ....1........1........1......1.......1.....1...1.1.1.1
%C A195805 ....1........1........1......1.......1.....1...1.1.1
%C A195805 ....2........3........4......5.......6.....7...8.9
%C A195805 ....8.......27.......64....125.....216...343.512
%C A195805 ...16......105......496...1759....5052.12469
%C A195805 ...64.....1695....24928.213319.1274808
%C A195805 .1184...284427.17528896
%C A195805 .5300.11606931
%e A195805 Some solutions for n=4 k=4
%e A195805 .....0........0........0........0........0........0........0........0
%e A195805 ....3.1......3.4......2.4......0.3......3.2......3.0......1.4......1.2
%e A195805 ...1.3.3....4.4.3....4.2.2....3.2.0....2.4.3....0.3.3....4.2.1....2.3.1
%e A195805 ..0.3.1.0..0.3.4.0..0.2.4.0..0.0.3.0..0.3.2.0..0.3.0.0..0.1.4.0..0.1.2.0
%K A195805 nonn,tabl
%O A195805 1,6
%A A195805 _R. H. Hardin_ Sep 23 2011