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A255657 Number of length n+5 0..3 arrays with at most two downsteps in every 5 consecutive neighbor pairs.

%I A255657 #10 Aug 23 2025 12:35:13
%S A255657 3340,11752,42653,155144,564600,2036844,7323894,26452984,95690028,
%T A255657 345980784,1250385422,4516046380,16313317592,58952879320,213036643465,
%U A255657 769783313248,2781411265212,10049660711008,36312457046956,131210437887132,474105380419912,1713085295392596
%N A255657 Number of length n+5 0..3 arrays with at most two downsteps in every 5 consecutive neighbor pairs.
%H A255657 R. H. Hardin, <a href="/A255657/b255657.txt">Table of n, a(n) for n = 1..210</a>
%F A255657 Empirical: a(n) = 4*a(n-1) -6*a(n-2) +20*a(n-3) -34*a(n-4) +148*a(n-5) -266*a(n-6) +192*a(n-7) -622*a(n-8) +1120*a(n-9) -3788*a(n-10) +6836*a(n-11) -5078*a(n-12) +3368*a(n-13) -1500*a(n-14) +1172*a(n-15) -603*a(n-16) +152*a(n-17) -376*a(n-18) +272*a(n-19) -156*a(n-20) +68*a(n-21) -10*a(n-22) +a(n-24).
%e A255657 Some solutions for n=4:
%e A255657 ..0....3....1....1....0....0....2....3....2....2....0....1....2....1....1....1
%e A255657 ..1....0....2....0....3....0....2....0....0....2....2....0....0....2....0....2
%e A255657 ..3....2....2....1....0....2....3....0....1....0....0....0....0....2....1....0
%e A255657 ..0....2....0....1....0....1....1....2....1....0....2....1....3....3....0....1
%e A255657 ..2....3....1....1....2....2....2....2....0....3....0....3....0....1....1....3
%e A255657 ..2....2....1....2....1....0....2....0....1....3....3....0....3....2....1....1
%e A255657 ..1....0....0....1....2....3....2....0....2....0....3....2....3....2....3....2
%e A255657 ..2....3....2....2....1....3....2....2....1....2....1....3....0....1....1....3
%e A255657 ..0....3....0....1....2....1....0....2....3....0....2....1....3....2....2....2
%Y A255657 Column 5 of A255660.
%K A255657 nonn,changed
%O A255657 1,1
%A A255657 _R. H. Hardin_, Mar 01 2015