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A202252 T(n,k)=Number of zero-sum -k..k arrays of n elements with adjacent element differences also in -k..k.

%I A202252 #7 Jul 22 2025 16:31:21
%S A202252 1,1,1,1,3,3,1,3,9,7,1,5,17,31,15,1,5,27,81,107,33,1,7,41,171,397,387,
%T A202252 75,1,7,57,309,1077,2003,1415,171,1,9,75,509,2385,6963,10239,5231,391,
%U A202252 1,9,97,779,4643,18841,45523,52697,19477,899,1,11,121,1133,8211,43293,150523
%N A202252 T(n,k)=Number of zero-sum -k..k arrays of n elements with adjacent element differences also in -k..k.
%C A202252 Table starts
%C A202252 ...1.....1.......1........1........1.........1..........1..........1
%C A202252 ...1.....3.......3........5........5.........7..........7..........9
%C A202252 ...3.....9......17.......27.......41........57.........75.........97
%C A202252 ...7....31......81......171......309.......509........779.......1133
%C A202252 ..15...107.....397.....1077.....2385......4643.......8211......13533
%C A202252 ..33...387....2003.....6963....18841.....43293......88301.....164873
%C A202252 ..75..1415...10239....45523...150523....408211.....960501....2031401
%C A202252 .171..5231...52697...300417..1212443...3882871...10536609...25247111
%C A202252 .391.19477..273021..1995897..9832015..37183105..116366779..315903491
%C A202252 .899.72933.1422337.13332697.80165217.358012837.1292162535.3974268379
%H A202252 R. H. Hardin, <a href="/A202252/b202252.txt">Table of n, a(n) for n = 1..9999</a>
%e A202252 Some solutions for n=6 k=7
%e A202252 ..0...-4....6....0...-3....0....2...-7....3...-3....0....5....3....0...-2...-4
%e A202252 ..4...-1....0....3...-5....7...-1...-1...-4...-6...-6....4....1....6...-4...-1
%e A202252 ..4...-1...-2....0...-4....0....4...-1...-2....0....1....3...-2....3....0....1
%e A202252 .-3....1...-3....4....2...-1....1....4...-3....6...-1...-2...-3...-4....6....6
%e A202252 ..1....0....0...-1....3...-3...-1....0....1....4....2...-4...-1...-2...-1....0
%e A202252 .-6....5...-1...-6....7...-3...-5....5....5...-1....4...-6....2...-3....1...-2
%Y A202252 Column 1 is A136029
%K A202252 nonn,tabl
%O A202252 1,5
%A A202252 _R. H. Hardin_ Dec 14 2011