cp's OEIS Frontend

A204214 Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.

%I A204214 #8 Jun 06 2018 11:35:31
%S A204214 21,120,404,1025,2181,4116,7120,11529,17725,26136,37236,51545,69629,
%T A204214 92100,119616,152881,192645,239704,294900,359121,433301,518420,615504,
%U A204214 725625,849901,989496,1145620,1319529,1512525,1725956,1961216,2219745
%N A204214 Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
%C A204214 Row 5 of A204213.
%H A204214 R. H. Hardin, <a href="/A204214/b204214.txt">Table of n, a(n) for n = 1..210</a>
%F A204214 Empirical: a(n) = (23/12)*n^4 + (37/6)*n^3 + (91/12)*n^2 + (13/3)*n + 1.
%F A204214 Conjectures from _Colin Barker_, Jun 06 2018: (Start)
%F A204214 G.f.: x*(21 + 15*x + 14*x^2 - 5*x^3 + x^4) / (1 - x)^5.
%F A204214 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 A204214 (End)
%e A204214 Some solutions for n=5:
%e A204214 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A204214 ..4....0....2....2....0....5....0....3....5....0....4....5....4....1....1....3
%e A204214 ..1....4....2....2....3....2....2....6....1....5....8...10....8....2....3....5
%e A204214 ..4....3....7....1....2....0....3....5....5....4....6...10....3....6....3....6
%e A204214 ..2....4....5....3....4....3....0....5....2....5....3....5....4....2....4....3
%e A204214 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%Y A204214 Cf. A204213.
%K A204214 nonn
%O A204214 1,1
%A A204214 _R. H. Hardin_, Jan 12 2012