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%I #4 Mar 01 2015 11:52:33
%S 16,64,64,255,256,256,968,1016,1024,1024,3340,3692,4048,4096,4096,
%T 10320,11752,14192,16128,16384,16384,28722,33042,42653,54560,64257,
%U 65536,65536,72920,83752,112196,155144,209412,256012,262144,262144,171106,195020
%N T(n,k)=Number of length n+k 0..3 arrays with at most two downsteps in every k consecutive neighbor pairs
%C Table starts
%C ......16.......64......255.......968......3340.....10320.....28722......72920
%C ......64......256.....1016......3692.....11752.....33042.....83752.....195020
%C .....256.....1024.....4048.....14192.....42653....112196....265430.....577464
%C ....1024.....4096....16128.....54560....155144....385738....864924....1788660
%C ....4096....16384....64257....209412....564600...1324872...2816673....5555336
%C ...16384....65536...256012....803246...2036844...4542671...9169016...17232696
%C ...65536...262144..1020000...3083292...7323894..15269184..29577432...53275408
%C ..262144..1048576..4063872..11835664..26452984..50963540..92530816..161617336
%C .1048576..4194304.16191231..45429680..95690028.171784096.286454024..471810032
%C .4194304.16777216.64508912.174365744.345980784.583245999.900260308.1359483102
%H R. H. Hardin, <a href="/A255660/b255660.txt">Table of n, a(n) for n = 1..9999</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1)
%F k=2: a(n) = 4*a(n-1)
%F k=3: a(n) = 4*a(n-1) -a(n-4)
%F k=4: [order 12]
%F k=5: [order 24]
%F k=6: [order 35]
%F k=7: [order 48]
%F Empirical for row n:
%F n=1: [polynomial of degree 11]
%F n=2: [polynomial of degree 11]
%F n=3: [polynomial of degree 11] for n>1
%F n=4: [polynomial of degree 11] for n>2
%F n=5: [polynomial of degree 11] for n>3
%F n=6: [polynomial of degree 11] for n>4
%F n=7: [polynomial of degree 11] for n>5
%e Some solutions for n=4 k=4
%e ..3....1....2....2....3....2....0....1....1....2....2....0....1....1....2....3
%e ..0....1....0....2....0....0....0....3....2....3....2....3....0....2....0....1
%e ..2....1....2....3....2....1....1....1....0....1....1....1....0....1....0....1
%e ..0....2....1....3....3....2....2....1....1....3....2....1....2....0....2....0
%e ..0....1....3....3....0....3....3....1....3....3....0....0....0....0....2....0
%e ..0....3....0....1....0....0....1....2....1....3....2....3....1....3....1....3
%e ..0....3....2....2....1....3....2....0....1....3....0....3....0....2....3....2
%e ..0....2....2....1....1....3....3....2....3....2....1....1....1....3....2....2
%Y Column 1 is A000302(n+1)
%Y Column 2 is A000302(n+2)
%Y Column 3 is A206450(n+3)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 01 2015
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