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%I #7 Sep 11 2018 05:41:24
%S 63,621,2511,6419,12947,22727,36471,54851,78539,108207,144527,188171,
%T 239811,300119,369767,449427,539771,641471,755199,881627,1021427,
%U 1175271,1343831,1527779,1727787,1944527,2178671,2430891,2701859,2992247,3302727
%N Number of third differences of arrays of length 6 of numbers in 0..n.
%H R. H. Hardin, <a href="/A228262/b228262.txt">Table of n, a(n) for n = 1..128</a>
%F Empirical: a(n) = 112*n^3 - 34*n^2 - 38*n - 13 for n>4.
%F Conjectures from _Colin Barker_, Sep 11 2018: (Start)
%F G.f.: x*(63 + 369*x + 405*x^2 - 151*x^3 - 84*x^4 + 30*x^5 + 80*x^6 - 40*x^7) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
%F (End)
%e Some solutions for n=4:
%e ..2...-9...-2....3....2..-12....7..-16..-10...-5....7....1....0...15...-1....0
%e ..7....4...-5....1...-4...13...-1...12...12....7..-10....5...-5..-10....8...-7
%e .-8....3....3...-7....2..-14....2...-1..-12..-10....4...-8...11....4...-9....3
%Y Row 3 of A228260.
%K nonn
%O 1,1
%A _R. H. Hardin_, Aug 19 2013
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