A200456 - OEIS

%I #8 May 21 2018 09:45:29

%S 4,44,142,342,678,1148,1832,2744,3874,5334,7114,9192,11708,14644,

%T 17962,21826,26206,31044,36544,42660,49310,56734,64866,73616,83256,

%U 93696,104834,116970,130006,143824,158748,174668,191446,209446,228542,248572

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

%C Row 2 of A200454.

%H R. H. Hardin, <a href="/A200456/b200456.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) +2*a(n-3) -2*a(n-4) +a(n-5) -2*a(n-6) +a(n-7) -2*a(n-8) +2*a(n-9) +a(n-11) -a(n-12).

%F Empirical g.f.: 2*(1 + x)*(2 + 18*x + 31*x^2 + 65*x^3 + 63*x^4 + 72*x^5 + 52*x^6 + 39*x^7 + 9*x^8 + 9*x^9) / ((1 - x)^4*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 21 2018

%e Some solutions for n=3:

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

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

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

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

%Y Cf. A200454.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 18 2011