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A203178 Number of n X 5 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above. 1

%I #7 Jul 28 2022 03:46:44

%S 3,6,41,205,952,4654,23083,115377,551208,2757161,13535075,66032042,

%T 327270427,1600093371,7879616025,38759698990,190148017740,

%U 936372926748,4597851371118,22603571928513,111146666196027,546043267710074

%N Number of n X 5 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.

%C Column 5 of A203181.

%H R. H. Hardin, <a href="/A203178/b203178.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-2) +116*a(n-3) +51*a(n-4) -167*a(n-5) -5304*a(n-6) -2099*a(n-7) -2525*a(n-8) +135828*a(n-9) +21391*a(n-10) +123514*a(n-11) -2093446*a(n-12) +97691*a(n-13) -1966033*a(n-14) +19493219*a(n-15) -3026365*a(n-16) +20145258*a(n-17) -113265090*a(n-18) +15159673*a(n-19) -114880900*a(n-20) +405552988*a(n-21) -19056386*a(n-22) +326124841*a(n-23) -748576479*a(n-24) -82472243*a(n-25) -466324510*a(n-26) +468742748*a(n-27) +186385862*a(n-28) +282899431*a(n-29) +170444820*a(n-30) -68888448*a(n-31) -45542936*a(n-32) -71161527*a(n-33) +37789114*a(n-34) -8127020*a(n-35) -13969563*a(n-36) +5855719*a(n-37) -3592899*a(n-38) -388368*a(n-39) +412490*a(n-40) -118958*a(n-41) +20064*a(n-42) -2340*a(n-43) for n>45.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A203181.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2011

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)