login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.
1

%I #8 May 21 2018 15:05:23

%S 41,295,1111,3011,6691,13021,23045,37981,59221,88331,127051,177295,

%T 241151,320881,418921,537881,680545,849871,1048991,1281211,1550011,

%U 1859045,2212141,2613301,3066701,3576691,4147795,4784711,5492311,6275641

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

%C Row 4 of A201042.

%H R. H. Hardin, <a href="/A201043/b201043.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (29/4)*n^4 + (29/2)*n^3 + (51/4)*n^2 + (11/2)*n + 1.

%F Conjectures from _Colin Barker_, May 21 2018: (Start)

%F G.f.: x*(41 + 90*x + 46*x^2 - 4*x^3 + x^4) / (1 - x)^5.

%F 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 (End)

%e Some solutions for n=7:

%e ..5...-5...-6...-2....2....3....1....5...-6...-3...-3....1....4...-2...-1...-1

%e .-1...-2...-3....3...-2...-2...-5...-1....0...-3....0....7...-3...-4...-5...-3

%e ..2....2....4....2...-1...-5....1....1...-4....2...-1....2....2...-4...-2...-7

%e ..1...-2....0....0....4....1....3...-1...-1....1....6...-4....6....2...-2...-1

%Y Cf. A201042.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2011