A204215 - OEIS

%I #9 Jun 06 2018 12:02:59

%S 51,473,2208,7167,18583,41363,82440,151125,259459,422565,659000,

%T 991107,1445367,2052751,2849072,3875337,5178099,6809809,8829168,

%U 11301479,14298999,17901291,22195576,27277085,33249411,40224861,48324808,57680043

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

%C Row 6 of A204213.

%H R. H. Hardin, <a href="/A204215/b204215.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (44/15)*n^5 + (133/12)*n^4 + 17*n^3 + (161/12)*n^2 + (167/30)*n + 1.

%F Conjectures from _Colin Barker_, Jun 06 2018: (Start)

%F G.f.: x*(51 + 167*x + 135*x^2 - 6*x^3 + 6*x^4 - x^5) / (1 - x)^6.

%F 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 (End)

%e Some solutions for n=5:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..3....1....3....3....5....5....4....2....4....4....4....0....4....1....0....3

%e ..5....6....5....4....6....5....2....3....3....8....9....0....3....3....1....5

%e ..4....4....3....3....6....7....4....6....5....7....7....3....6....4....5....5

%e ..5....5....7....2....8....7....4....1....4....4....6....1....5....0....0....2

%e ..3....1....5....0....3....5....0....1....0....0....4....5....2....2....3....1

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%Y Cf. A204213.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 12 2012