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A255658 Number of length n+6 0..3 arrays with at most two downsteps in every 6 consecutive neighbor pairs.

%I A255658 #6 Jul 23 2025 15:09:02
%S A255658 10320,33042,112196,385738,1324872,4542671,15269184,50963540,
%T A255658 171784096,583245999,1978627688,6707590534,22709921860,76722468914,
%U A255658 259180579024,877068284264,2969801621944,10051964251804,34016225117956
%N A255658 Number of length n+6 0..3 arrays with at most two downsteps in every 6 consecutive neighbor pairs.
%C A255658 Column 6 of A255660
%H A255658 R. H. Hardin, <a href="/A255658/b255658.txt">Table of n, a(n) for n = 1..210</a>
%F A255658 Empirical: a(n) = 4*a(n-1) -6*a(n-2) +20*a(n-3) -34*a(n-4) +24*a(n-5) +230*a(n-6) -552*a(n-7) +447*a(n-8) -4060*a(n-9) +6908*a(n-10) -2648*a(n-11) -10346*a(n-12) +26292*a(n-13) -21776*a(n-14) +185776*a(n-15) -406128*a(n-16) +326996*a(n-17) -196764*a(n-18) +82488*a(n-19) -13045*a(n-20) -115472*a(n-21) +108636*a(n-22) -29312*a(n-23) +73724*a(n-24) -12420*a(n-25) -41050*a(n-26) +38840*a(n-27) -21680*a(n-28) +3232*a(n-29) -12984*a(n-30) +13080*a(n-31) -4064*a(n-32) +320*a(n-34) +64*a(n-35)
%e A255658 Some solutions for n=3
%e A255658 ..0....0....1....3....0....1....3....2....2....2....0....3....0....2....0....0
%e A255658 ..2....1....0....0....3....1....0....3....3....2....0....2....0....0....2....1
%e A255658 ..2....1....2....2....0....0....2....1....3....3....1....3....0....2....3....0
%e A255658 ..3....0....3....2....0....2....3....3....3....2....1....1....0....2....2....0
%e A255658 ..3....1....3....3....1....0....0....3....0....1....1....2....0....0....0....0
%e A255658 ..0....0....1....0....3....0....2....0....2....1....3....2....0....3....0....2
%e A255658 ..3....0....1....0....3....2....2....3....2....2....2....3....2....3....1....3
%e A255658 ..1....2....2....3....3....3....2....3....2....2....0....3....3....2....1....2
%e A255658 ..2....2....1....2....2....2....1....3....0....3....3....2....1....2....1....2
%Y A255658 Cf. A255660
%K A255658 nonn
%O A255658 1,1
%A A255658 _R. H. Hardin_, Mar 01 2015