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A201089 Number of -n..n arrays of 4 elements with first and second differences also in -n..n.

%I A201089 #11 Feb 14 2018 15:00:34
%S A201089 25,175,651,1759,3899,7581,13405,22085,34421,51331,73815,102995,
%T A201089 140071,186369,243289,312361,395185,493495,609091,743911,899955,
%U A201089 1079365,1284341,1517229,1780429,2076491,2408015,2777755,3188511,3643241,4144945,4696785
%N A201089 Number of -n..n arrays of 4 elements with first and second differences also in -n..n.
%C A201089 Row 4 of A201088.
%H A201089 R. H. Hardin, <a href="/A201089/b201089.txt">Table of n, a(n) for n = 1..210</a>
%F A201089 Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7).
%F A201089 Empirical: -x*(25+100*x+151*x^2+106*x^3+23*x^4-2*x^5+x^6) / ( (1+x)^2*(x-1)^5 ). - _R. J. Mathar_, Nov 27 2011
%F A201089 Conjectures from _Colin Barker_, Feb 14 2018: (Start)
%F A201089 a(n) = (101*n^4 + 202*n^3 + 190*n^2 + 92*n + 24) / 24 for n even.
%F A201089 a(n) = (101*n^4 + 202*n^3 + 190*n^2 + 86*n + 21) / 24 for n odd.
%F A201089 (End)
%e A201089 Some solutions for n=8:
%e A201089 ..3....6....5....5....5....1....7...-3....3....6...-5....0....1...-8....4...-5
%e A201089 ..0....6...-1....5....0....0...-1....0....6....7...-4....2....0...-4....6...-3
%e A201089 ..2...-1...-6....7....2...-3...-7....1....7....3...-4....1...-5....1....2...-3
%e A201089 ..7...-2...-5....6...-2...-2...-8...-5....0....6....2...-3...-8....1....3...-7
%K A201089 nonn
%O A201089 1,1
%A A201089 _R. H. Hardin_, Nov 26 2011