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A188249 T(n,k)=Number of arrangements of n+2 nonzero numbers x(i) in -k..k with the sum of x(i)*x(i+1) equal to zero.

%I A188249 #7 Jul 22 2025 11:05:24
%S A188249 4,16,0,36,20,12,64,52,120,0,100,144,548,300,40,144,208,1504,1632,
%T A188249 1284,0,196,436,3292,7092,12692,4132,140,256,532,6376,16484,58824,
%U A188249 51196,16272,0,324,816,10564,43440,193232,368588,355396,57808,504,400,1072,17040,75080
%N A188249 T(n,k)=Number of arrangements of n+2 nonzero numbers x(i) in -k..k with the sum of x(i)*x(i+1) equal to zero.
%C A188249 Table starts
%C A188249 ...4.....16.......36.........64.........100.........144..........196
%C A188249 ...0.....20.......52........144.........208.........436..........532
%C A188249 ..12....120......548.......1504........3292........6376........10564
%C A188249 ...0....300.....1632.......7092.......16484.......43440........75080
%C A188249 ..40...1284....12692......58824......193232......521124......1142180
%C A188249 ...0...4132....51196.....368588.....1399640.....4875112.....11953848
%C A188249 .140..16272...355396....2880240....14715004....55994544....168083116
%C A188249 ...0..57808..1657632...20265640...123729664...591604824...2026547348
%C A188249 .504.223308.10858368..156028036..1247614580..6764014136..27843005992
%C A188249 ...0.828456.54754656.1154193268.11199296500.75116513672.355600251460
%H A188249 R. H. Hardin, <a href="/A188249/b188249.txt">Table of n, a(n) for n = 1..159</a>
%e A188249 Some solutions for n=6 k=4
%e A188249 .-2...-3...-3...-1...-2...-1....1....2...-3...-4....3...-4...-2...-4...-4...-2
%e A188249 .-2...-4...-4...-4...-4...-4...-4...-4...-2...-3...-4...-3...-3...-4...-3...-4
%e A188249 .-3...-2...-2....4....3....2....1....1...-4....3...-2....1....3....2....1....2
%e A188249 .-4...-2...-1...-1....1...-1....2...-4....2...-4....1...-3...-1....2....4....4
%e A188249 ..3....4...-4...-4...-2...-2...-1...-2...-2...-3....1....1...-2...-1....2...-3
%e A188249 .-2...-4....2...-3....1...-2...-2...-3....4....3....4...-3...-3....1...-3...-4
%e A188249 ..1...-3...-3...-3....1...-2...-1....2....3....3....1....3...-2....3....3....4
%e A188249 .-2....4....4....3....4....2...-4....4...-2...-1...-3....3....4...-4...-2....2
%Y A188249 Column 1 is 4*A138364
%K A188249 nonn,tabl
%O A188249 1,1
%A A188249 _R. H. Hardin_ Mar 25 2011