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A201043 Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.

%I A201043 #8 May 21 2018 15:05:23
%S A201043 41,295,1111,3011,6691,13021,23045,37981,59221,88331,127051,177295,
%T A201043 241151,320881,418921,537881,680545,849871,1048991,1281211,1550011,
%U A201043 1859045,2212141,2613301,3066701,3576691,4147795,4784711,5492311,6275641
%N A201043 Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.
%C A201043 Row 4 of A201042.
%H A201043 R. H. Hardin, <a href="/A201043/b201043.txt">Table of n, a(n) for n = 1..210</a>
%F A201043 Empirical: a(n) = (29/4)*n^4 + (29/2)*n^3 + (51/4)*n^2 + (11/2)*n + 1.
%F A201043 Conjectures from _Colin Barker_, May 21 2018: (Start)
%F A201043 G.f.: x*(41 + 90*x + 46*x^2 - 4*x^3 + x^4) / (1 - x)^5.
%F A201043 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A201043 (End)
%e A201043 Some solutions for n=7:
%e A201043 ..5...-5...-6...-2....2....3....1....5...-6...-3...-3....1....4...-2...-1...-1
%e A201043 .-1...-2...-3....3...-2...-2...-5...-1....0...-3....0....7...-3...-4...-5...-3
%e A201043 ..2....2....4....2...-1...-5....1....1...-4....2...-1....2....2...-4...-2...-7
%e A201043 ..1...-2....0....0....4....1....3...-1...-1....1....6...-4....6....2...-2...-1
%Y A201043 Cf. A201042.
%K A201043 nonn
%O A201043 1,1
%A A201043 _R. H. Hardin_, Nov 26 2011