cp's OEIS Frontend

A228222 Number of second differences of arrays of length 7 of numbers in 0..n.

%I A228222 #8 Sep 10 2018 08:39:26
%S A228222 127,2059,14053,58141,176851,439927,951049,1854553,3342151,5659651,
%T A228222 9113677,14078389,21002203,30414511,42932401,59267377,80232079,
%U A228222 106747003,139847221,180689101,230557027,290870119,363188953,449222281,550833751
%N A228222 Number of second differences of arrays of length 7 of numbers in 0..n.
%H A228222 R. H. Hardin, <a href="/A228222/b228222.txt">Table of n, a(n) for n = 1..63</a>
%F A228222 Empirical: a(n) = 56*n^5 + 14*n^4 - 108*n^3 + 289*n^2 - 125*n + 1.
%F A228222 Conjectures from _Colin Barker_, Sep 10 2018: (Start)
%F A228222 G.f.: x*(127 + 1297*x + 3604*x^2 + 2168*x^3 - 475*x^4 - x^5) / (1 - x)^6.
%F A228222 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A228222 (End)
%e A228222 Some solutions for n=4:
%e A228222 .-7....5...-3....1...-2...-1....1....5...-1....3....6...-6....5....0....5...-1
%e A228222 ..2...-1....1...-2....2....0...-1...-6...-1...-1...-3....5....2....1....0....2
%e A228222 ..2...-1...-2....5...-2...-2....2....4....6...-1....4....1...-6....3...-5....0
%e A228222 .-2...-1...-1...-7....3....0....0...-6...-8....3...-3...-2....4...-4....5...-5
%e A228222 ..4....2....3....5...-2....4....0....4....6...-6...-3...-3....1....1...-1....8
%Y A228222 Row 5 of A228218.
%K A228222 nonn
%O A228222 1,1
%A A228222 _R. H. Hardin_, Aug 16 2013