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A201045 Number of -n..n arrays of 6 elements with adjacent element differences also in -n..n.

%I A201045 #9 May 22 2018 03:49:35
%S A201045 239,4569,33305,148433,491429,1333683,3139529,6641881,12930475,
%T A201045 23552717,40627137,66969449,106231217,163051127,243218865,353851601,
%U A201045 503583079,702765313,963682889,1300779873,1730899325,2273535419,2951098169
%N A201045 Number of -n..n arrays of 6 elements with adjacent element differences also in -n..n.
%C A201045 Row 6 of A201042.
%H A201045 R. H. Hardin, <a href="/A201045/b201045.txt">Table of n, a(n) for n = 1..210</a>
%F A201045 Empirical: a(n) = (2101/120)*n^6 + (2101/40)*n^5 + (1753/24)*n^4 + (1405/24)*n^3 + (569/20)*n^2 + (119/15)*n + 1.
%F A201045 Conjectures from _Colin Barker_, May 22 2018: (Start)
%F A201045 G.f.: x*(239 + 2896*x + 6341*x^2 + 2882*x^3 + 253*x^4 - 6*x^5 + x^6) / (1 - x)^7.
%F A201045 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A201045 (End)
%e A201045 Some solutions for n=3:
%e A201045 .-2...-1....1....3...-1....2...-1...-2....2....2...-2....0....1....0....1...-3
%e A201045 ..1...-2....1....1...-2....3....2....0....2....0....1...-2....2....1...-2...-1
%e A201045 .-1...-2...-1....1...-3....3....3...-2....2...-2....0....1....1...-1....1....2
%e A201045 .-3...-3....1....1...-2....2....1...-1....1...-1....1....0....1...-2...-1....0
%e A201045 .-3...-1....3....3...-1....2...-2...-2....0...-2...-1...-3...-1....1...-3...-1
%e A201045 .-2....0....0....1....1....3....1...-1....3...-3...-1...-1....0...-1....0...-1
%Y A201045 Cf. A201042.
%K A201045 nonn
%O A201045 1,1
%A A201045 _R. H. Hardin_, Nov 26 2011