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A201989 T(n,k) is the number of n X k zero-sum -3..3 arrays with rows and columns lexicographically nondecreasing.

%I A201989 #8 Jan 30 2025 15:45:54
%S A201989 1,4,4,8,77,8,18,1170,1170,18,32,14107,134217,14107,32,58,139471,
%T A201989 11648559,11648559,139471,58,94,1177568,803133854,7375608084,
%U A201989 803133854,1177568,94,151,8721417,46034224561,3674187761233,3674187761233
%N A201989 T(n,k) is the number of n X k zero-sum -3..3 arrays with rows and columns lexicographically nondecreasing.
%H A201989 R. H. Hardin, <a href="/A201989/b201989.txt">Table of n, a(n) for n = 1..59</a>
%e A201989 Table starts:
%e A201989 ...1........4..............8.................18...................32
%e A201989 ...4.......77...........1170..............14107...............139471
%e A201989 ...8.....1170.........134217...........11648559............803133854
%e A201989 ..18....14107.......11648559.........7375608084........3674187761233
%e A201989 ..32...139471......803133854......3674187761233....13189629907532856
%e A201989 ..58..1177568....46034224561...1507315600099908.38785259210265819578
%e A201989 ..94..8721417..2263314310579.526500713340421071
%e A201989 .151.57801225.97590406110264
%e A201989 Some solutions for n=3 and k=3:
%e A201989 .-3..2..2...-3.-1..3...-3.-3..2...-3.-1..1...-2..0..2...-3.-1..1...-3.-3.-3
%e A201989 ..1.-2.-1...-3..1.-2...-1..0..1....0.-3..2...-2..3.-1....1..2.-3....1..2..3
%e A201989 ..3.-2..0....0..2..3....0..1..3....2..2..0...-1.-1..2....3..2.-2....2.-1..2
%Y A201989 Column 1 is A001977.
%K A201989 nonn,tabl
%O A201989 1,2
%A A201989 _R. H. Hardin_, Dec 07 2011