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A228223 Number of second differences of arrays of length 8 of numbers in 0..n.

%I A228223 #8 Sep 10 2018 08:51:49
%S A228223 255,6305,58975,320481,1225631,3693505,9399615,21108545,43067071,
%T A228223 81457761,144913055,245089825,397304415,621228161,941643391,
%U A228223 1389259905,2001591935,2823895585,3910166751,5324199521,7140705055,9446490945
%N A228223 Number of second differences of arrays of length 8 of numbers in 0..n.
%H A228223 R. H. Hardin, <a href="/A228223/b228223.txt">Table of n, a(n) for n = 1..34</a>
%F A228223 Empirical: a(n) = 84*n^6 - 402*n^4 + 1656*n^3 - 1860*n^2 + 776*n + 1.
%F A228223 Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F A228223 G.f.: x*(255 + 4520*x + 20195*x^2 + 31136*x^3 + 8989*x^4 - 4616*x^5 + x^6) / (1 - x)^7.
%F A228223 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 A228223 (End)
%e A228223 Some solutions for n=4:
%e A228223 .-4...-4...-8...-2...-2....0....0...-4....0...-6...-4....0...-6...-2...-4...-4
%e A228223 .-1....7....5....4....1....0...-4...-3....0....0....7...-4....6....3....0....7
%e A228223 ..4...-5....1...-6...-2...-3....8....2....1....5...-6....3...-4...-1....2...-6
%e A228223 .-2....2...-2....3....0....5...-4....2...-4...-6....1...-2....1...-1....0....4
%e A228223 .-2...-4....0....0...-1...-3...-1...-2....4....7....4....1...-1...-2....3....1
%e A228223 ..2....4....1....2....3...-2....2....4...-1...-4...-5...-1....0....0...-6...-3
%Y A228223 Row 6 of A228218.
%K A228223 nonn
%O A228223 1,1
%A A228223 _R. H. Hardin_, Aug 16 2013