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 A200205 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second and third differences. 1

%I #9 May 20 2018 12:23:47

%S 12,68,186,422,798,1316,2064,3048,4254,5802,7682,9864,12500,15564,

%T 19010,23022,27558,32556,38232,44528,51366,58994,67338,76304,86172,

%U 96852,108234,120630,133934,148020,163232,179448,196526,214842,234258,254616

%N Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero second and third differences.

%C Row 1 of A200204.

%H R. H. Hardin, <a href="/A200205/b200205.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -4*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8).

%F Empirical g.f.: 2*x*(6 + 22*x + 31*x^2 + 47*x^3 + 26*x^4 + 9*x^5 + 3*x^6) / ((1 - x)^4*(1 + x + x^2)^2). - _Colin Barker_, May 20 2018

%e Some solutions for n=3:

%e .-1....1....2....1...-3....2....2...-1....0....0....2....2....1...-2....1....1

%e ..3...-2....2...-1....1....2....2...-3...-2....3....0...-1....3....1...-3...-2

%e .-1....0...-1....3....3...-2...-3....2....3...-2...-3...-2...-3....0....1....3

%e .-1....1...-3...-3...-1...-2...-1....2...-1...-1....1....1...-1....1....1...-2

%Y Cf. A200204.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2011

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Last modified September 8 12:42 EDT 2024. Contains 375753 sequences. (Running on oeis4.)