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A201044 Number of -n..n arrays of 5 elements with adjacent element differences also in -n..n.

%I A201044 #8 May 22 2018 03:34:04
%S A201044 99,1161,6083,21141,57343,131781,268983,502265,875083,1442385,2271963,
%T A201044 3445805,5061447,7233325,10094127,13796145,18512627,24439129,31794867,
%U A201044 40824069,51797327,65012949,80798311,99511209,121541211,147311009
%N A201044 Number of -n..n arrays of 5 elements with adjacent element differences also in -n..n.
%C A201044 Row 5 of A201042.
%H A201044 R. H. Hardin, <a href="/A201044/b201044.txt">Table of n, a(n) for n = 1..210</a>
%F A201044 Empirical: a(n) = (169/15)*n^5 + (169/6)*n^4 + 32*n^3 + (119/6)*n^2 + (101/15)*n + 1.
%F A201044 Conjectures from _Colin Barker_, May 22 2018: (Start)
%F A201044 G.f.: x*(99 + 567*x + 602*x^2 + 78*x^3 + 7*x^4 - x^5) / (1 - x)^6.
%F A201044 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A201044 (End)
%e A201044 Some solutions for n=5:
%e A201044 .-5...-3...-4...-2...-3...-4...-1...-4...-4....5...-5...-1...-1....0...-2...-1
%e A201044 .-1....0...-2....2....2...-4...-2....0...-2....0...-2....0...-3....0....1....0
%e A201044 .-5....0....1....2...-2....1...-1...-2...-1....2...-2....2...-2...-3....0....1
%e A201044 ..0....5...-4...-2....3...-2...-2...-3...-2....1....1....1...-2...-5....0...-4
%e A201044 .-4....1...-5....1....0...-1...-4....0....0....5....0....0...-5...-2...-3...-2
%Y A201044 Cf. A201042.
%K A201044 nonn
%O A201044 1,1
%A A201044 _R. H. Hardin_, Nov 26 2011