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A255659 Number of length n+7 0..3 arrays with at most two downsteps in every 7 consecutive neighbor pairs.

%I A255659 #6 Jul 23 2025 15:09:09
%S A255659 28722,83752,265430,864924,2816673,9169016,29577432,92530816,
%T A255659 286454024,900260308,2873064972,9187712072,29298245258,93413733472,
%U A255659 297026093532,940176646792,2973476370798,9435365703664,30019424281120,95485615550472
%N A255659 Number of length n+7 0..3 arrays with at most two downsteps in every 7 consecutive neighbor pairs.
%C A255659 Column 7 of A255660
%H A255659 R. H. Hardin, <a href="/A255659/b255659.txt">Table of n, a(n) for n = 1..210</a>
%F A255659 Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) +30*a(n-4) -72*a(n-5) +58*a(n-6) +872*a(n-7) -2121*a(n-8) +1748*a(n-9) -492*a(n-10) -13640*a(n-11) +26816*a(n-12) -13536*a(n-13) -232948*a(n-14) +493540*a(n-15) -280547*a(n-16) -33840*a(n-17) +1271000*a(n-18) -2599020*a(n-19) +2012477*a(n-20) +14744048*a(n-21) -38149820*a(n-22) +32418288*a(n-23) -9358211*a(n-24) -17204016*a(n-25) +20480444*a(n-26) -6417756*a(n-27) -25522136*a(n-28) +31264272*a(n-29) -10417774*a(n-30) -104220*a(n-31) +17617480*a(n-32) -9721216*a(n-33) -6417184*a(n-34) +19052720*a(n-35) -11470236*a(n-36) -3073784*a(n-37) +2563240*a(n-38) -4701200*a(n-39) +5023520*a(n-40) -1940960*a(n-41) -2778800*a(n-42) +3580160*a(n-43) -1109600*a(n-44) +16000*a(n-45) +88000*a(n-46) +22400*a(n-47) +10000*a(n-48)
%e A255659 Some solutions for n=2
%e A255659 ..0....0....2....0....3....3....0....0....2....3....1....0....2....2....1....0
%e A255659 ..0....1....3....0....3....0....1....3....2....1....2....0....0....0....3....2
%e A255659 ..0....2....0....2....3....2....0....1....3....2....2....3....2....0....3....3
%e A255659 ..3....1....2....2....0....2....0....1....3....3....2....0....2....2....2....3
%e A255659 ..1....1....3....2....0....1....0....0....3....1....2....2....3....1....2....3
%e A255659 ..1....3....0....0....1....1....0....3....0....1....2....2....3....2....1....1
%e A255659 ..3....3....2....2....3....2....0....3....2....2....0....0....3....3....2....1
%e A255659 ..3....0....3....2....0....3....1....3....1....3....3....0....1....3....2....0
%e A255659 ..2....3....3....3....0....2....0....3....1....3....1....0....0....1....3....3
%Y A255659 Cf. A255660
%K A255659 nonn
%O A255659 1,1
%A A255659 _R. H. Hardin_, Mar 01 2015