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A204215 Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.

%I A204215 #9 Jun 06 2018 12:02:59
%S A204215 51,473,2208,7167,18583,41363,82440,151125,259459,422565,659000,
%T A204215 991107,1445367,2052751,2849072,3875337,5178099,6809809,8829168,
%U A204215 11301479,14298999,17901291,22195576,27277085,33249411,40224861,48324808,57680043
%N A204215 Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
%C A204215 Row 6 of A204213.
%H A204215 R. H. Hardin, <a href="/A204215/b204215.txt">Table of n, a(n) for n = 1..210</a>
%F A204215 Empirical: a(n) = (44/15)*n^5 + (133/12)*n^4 + 17*n^3 + (161/12)*n^2 + (167/30)*n + 1.
%F A204215 Conjectures from _Colin Barker_, Jun 06 2018: (Start)
%F A204215 G.f.: x*(51 + 167*x + 135*x^2 - 6*x^3 + 6*x^4 - x^5) / (1 - x)^6.
%F A204215 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 A204215 (End)
%e A204215 Some solutions for n=5:
%e A204215 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A204215 ..3....1....3....3....5....5....4....2....4....4....4....0....4....1....0....3
%e A204215 ..5....6....5....4....6....5....2....3....3....8....9....0....3....3....1....5
%e A204215 ..4....4....3....3....6....7....4....6....5....7....7....3....6....4....5....5
%e A204215 ..5....5....7....2....8....7....4....1....4....4....6....1....5....0....0....2
%e A204215 ..3....1....5....0....3....5....0....1....0....0....4....5....2....2....3....1
%e A204215 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y A204215 Cf. A204213.
%K A204215 nonn
%O A204215 1,1
%A A204215 _R. H. Hardin_, Jan 12 2012