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A255666 Number of length n+6 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs.

%I A255666 #6 Jul 23 2025 15:09:37
%S A255666 16384,65536,256012,803246,2036844,4542671,9169016,17232696,30665992,
%T A255666 52227111,85761364,136522338,211563872,320215410,474655320,690599060,
%U A255666 988121664,1392636938,1936059024,2658175636,3608266324,4847003609
%N A255666 Number of length n+6 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C A255666 Row 6 of A255660
%H A255666 R. H. Hardin, <a href="/A255666/b255666.txt">Table of n, a(n) for n = 1..210</a>
%F A255666 Empirical: a(n) = (1/39916800)*n^11 + (1/302400)*n^10 + (143/725760)*n^9 + (137/20160)*n^8 + (686191/1209600)*n^7 + (68821/4800)*n^6 + (118924709/725760)*n^5 + (37326349/60480)*n^4 + (9666601859/907200)*n^3 - (165778309/8400)*n^2 + (24588142/3465)*n - 6396 for n>4
%e A255666 Some solutions for n=2
%e A255666 ..1....2....0....0....1....2....1....0....0....2....3....3....2....2....2....3
%e A255666 ..0....3....3....1....1....3....1....0....2....0....2....1....3....3....3....3
%e A255666 ..3....3....2....1....0....2....0....3....3....2....2....1....0....1....1....0
%e A255666 ..3....0....0....3....0....3....2....0....3....2....3....1....0....3....3....3
%e A255666 ..1....2....0....0....2....1....2....3....1....1....1....2....2....1....0....2
%e A255666 ..0....3....0....1....0....3....2....0....2....3....2....3....1....3....3....3
%e A255666 ..2....2....0....1....2....1....1....1....3....2....1....1....0....1....3....0
%e A255666 ..0....1....0....1....3....2....1....1....0....3....0....1....0....2....0....0
%Y A255666 Cf. A255660
%K A255666 nonn
%O A255666 1,1
%A A255666 _R. H. Hardin_, Mar 01 2015