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A228224 Number of second differences of arrays of length 9 of numbers in 0..n.

%I A228224 #10 Sep 10 2018 08:52:30
%S A228224 511,19171,242461,1688101,8006491,29066311,86929081,224817481,
%T A228224 519682231,1098972331,2162213461,4007999341,7067000851,11941597711,
%U A228224 19452737521,30694626961,47097859951,70501587571,103235334541,148211067061
%N A228224 Number of second differences of arrays of length 9 of numbers in 0..n.
%H A228224 R. H. Hardin, <a href="/A228224/b228224.txt">Table of n, a(n) for n = 1..24</a>
%F A228224 Empirical: a(n) = 120*n^7 - 42*n^6 - 1158*n^5 + 6945*n^4 - 13980*n^3 + 13512*n^2 - 4887*n + 1.
%F A228224 Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F A228224 G.f.: x*(511 + 15083*x + 103401*x^2 + 256585*x^3 + 252785*x^4 + 16749*x^5 - 40313*x^6 - x^7) / (1 - x)^8.
%F A228224 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A228224 (End)
%e A228224 Some solutions for n=4:
%e A228224 .-6...-4...-8...-6...-4...-6...-6...-6...-4...-6...-6...-6...-4...-6...-4...-4
%e A228224 ..2....2....7....6....0....5....1....6...-4....6....4....7...-2....5....2...-4
%e A228224 ..5....2...-6...-4....0....2....0...-3....6...-4...-3...-5....4....0...-4....8
%e A228224 .-4...-2....3....1....3...-4....3....0...-1....1....6....3...-2...-3....5...-7
%e A228224 .-3....0....0...-3...-5....1...-3...-3...-1...-1...-4...-3...-1....2...-3....3
%e A228224 ..3....2....0....3....3....0....1....3....1....4...-3....3....2...-3....0....0
%e A228224 .-1...-2....2....0....1...-2....0....1...-4...-4....4...-2...-4....0....4....0
%Y A228224 Row 7 of A228218.
%K A228224 nonn
%O A228224 1,1
%A A228224 _R. H. Hardin_, Aug 16 2013