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Number of length n+5 0..3 arrays with at most two downsteps in every 5 consecutive neighbor pairs
1

%I #4 Mar 01 2015 11:50:24

%S 3340,11752,42653,155144,564600,2036844,7323894,26452984,95690028,

%T 345980784,1250385422,4516046380,16313317592,58952879320,213036643465,

%U 769783313248,2781411265212,10049660711008,36312457046956

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

%C Column 5 of A255660

%H R. H. Hardin, <a href="/A255657/b255657.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Some solutions for n=4

%e ..0....3....1....1....0....0....2....3....2....2....0....1....2....1....1....1

%e ..1....0....2....0....3....0....2....0....0....2....2....0....0....2....0....2

%e ..3....2....2....1....0....2....3....0....1....0....0....0....0....2....1....0

%e ..0....2....0....1....0....1....1....2....1....0....2....1....3....3....0....1

%e ..2....3....1....1....2....2....2....2....0....3....0....3....0....1....1....3

%e ..2....2....1....2....1....0....2....0....1....3....3....0....3....2....1....1

%e ..1....0....0....1....2....3....2....0....2....0....3....2....3....2....3....2

%e ..2....3....2....2....1....3....2....2....1....2....1....3....0....1....1....3

%e ..0....3....0....1....2....1....0....2....3....0....2....1....3....2....2....2

%Y Cf. A255660

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 01 2015