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Number of -n..n arrays x(0..4) of 5 elements with nonzero sum and with zero through 4 differences all nonzero
1

%I #5 Mar 31 2012 12:36:38

%S 2,276,2778,15040,52486,145482,336992,695778,1309052,2298830,3808116,

%T 6034796,9189086,13554364,19435742,27212132,37285690,50170962,

%U 66371288,86532042,111309444,141482278,177842124,221369312,272987306,333851184

%N Number of -n..n arrays x(0..4) of 5 elements with nonzero sum and with zero through 4 differences all nonzero

%C Row 5 of A200165

%H R. H. Hardin, <a href="/A200168/b200168.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = -a(n-1) -2*a(n-2) -a(n-3) -a(n-4) +a(n-5) +2*a(n-6) +3*a(n-7) +3*a(n-8) +3*a(n-9) +2*a(n-10) +2*a(n-11) +a(n-12) +a(n-13) -a(n-15) -a(n-16) -3*a(n-17) -2*a(n-18) -4*a(n-19) -3*a(n-20) -5*a(n-21) -4*a(n-22) -5*a(n-23) -3*a(n-24) -3*a(n-25) +3*a(n-28) +3*a(n-29) +5*a(n-30) +5*a(n-31) +6*a(n-32) +6*a(n-33) +5*a(n-34) +5*a(n-35) +3*a(n-36) +3*a(n-37) -3*a(n-40) -3*a(n-41) -5*a(n-42) -4*a(n-43) -5*a(n-44) -3*a(n-45) -4*a(n-46) -2*a(n-47) -3*a(n-48) -a(n-49) -a(n-50) +a(n-52) +a(n-53) +2*a(n-54) +2*a(n-55) +3*a(n-56) +3*a(n-57) +3*a(n-58) +2*a(n-59) +a(n-60) -a(n-61) -a(n-62) -2*a(n-63) -a(n-64) -a(n-65)

%e Some solutions for n=5

%e .-5....5...-3...-1...-5....3...-5...-3...-4....4....5....4...-1....1...-3....3

%e ..5...-1...-5....4....1....4....5....4....1....1....2....5....3....4...-5....4

%e .-4....1....3...-5...-2...-4...-1...-3....4....3....5...-3....2....2....3...-2

%e ..2...-5...-2....4....1....5....4...-5...-4....1...-1...-4....4...-1...-4...-3

%e ..4...-3...-3...-5....3...-4....3...-3....5...-4....4....3....2....3...-1...-5

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 13 2011