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A228221 Number of second differences of arrays of length 6 of numbers in 0..n.

%I A228221 #7 Sep 10 2018 05:44:14
%S A228221 63,665,3151,9705,23351,47953,88215,149681,238735,362601,529343,
%T A228221 747865,1027911,1380065,1815751,2347233,2987615,3750841,4651695,
%U A228221 5705801,6929623,8340465,9956471,11796625,13880751,16229513,18864415,21807801,25082855
%N A228221 Number of second differences of arrays of length 6 of numbers in 0..n.
%H A228221 R. H. Hardin, <a href="/A228221/b228221.txt">Table of n, a(n) for n = 1..177</a>
%F A228221 Empirical: a(n) = 35*n^4 + 14*n^3 - 17*n^2 + 30*n + 1.
%F A228221 Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F A228221 G.f.: x*(63 + 350*x + 456*x^2 - 30*x^3 + x^4) / (1 - x)^5.
%F A228221 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A228221 (End)
%e A228221 Some solutions for n=4:
%e A228221 ..4....5....6...-2...-5....5...-6....5....7...-2....0....3...-1....4...-2....3
%e A228221 ..0...-2...-3...-3...-1....0....3...-3...-5....3...-4...-5....5....0....1...-2
%e A228221 .-4....5....0....1....2...-4....2....3....5...-1....4....0...-6...-3....1...-2
%e A228221 ..1...-8....5....1...-1....2...-5...-4...-7...-2....2....3....7....0....4....4
%Y A228221 Row 4 of A228218.
%K A228221 nonn
%O A228221 1,1
%A A228221 _R. H. Hardin_, Aug 16 2013