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%I #11 Aug 10 2015 17:56:59
%S 13,27,27,53,49,53,107,87,87,107,213,161,143,161,213,427,299,247,247,
%T 299,427,853,565,433,401,433,565,853,1707,1075,777,667,667,777,1075,
%U 1707,3413,2065,1413,1141,1061,1141,1413,2065,3413,6827,3991,2607,1987,1743
%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
%C Table starts:
%C ...13...27...53...107...213...427...853..1707..3413...6827..13653..27307..54613
%C ...27...49...87...161...299...565..1075..2065..3991...7761..15163..29749..58563
%C ...53...87..143...247...433...777..1413..2607..4863...9167..17433..33417..64493
%C ..107..161..247...401...667..1141..1987..3521..6327..11521..21227..39541..74387
%C ..213..299..433...667..1061..1743..2925..5003..8689..15307..27317..49359..90237
%C ..427..565..777..1141..1743..2763..4491..7453.12569..21501..37255..65355.116035
%C ..853.1075.1413..1987..2925..4491..7101.11491.18917..31587..53389..91275.157789
%C .1707.2065.2607..3521..5003..7453.11491.18193.29359..48081..79675.133405.225555
%C .3413.3991.4863..6327..8689.12569.18917.29359.46575..75087.122521.201881.335501
%C .6827.7761.9167.11521.15307.21501.31587.48081.75087.119441.192507.313341.514067
%H R. H. Hardin, <a href="/A251149/b251149.txt">Table of n, a(n) for n = 1..364</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +2*a(n-2)
%F k=2: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%F k=3: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%F k=4: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%F k=5: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%F k=6: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%F k=7: a(n) = 3*a(n-1) -5*a(n-3) +a(n-4) +2*a(n-5)
%e Some solutions for n=4, k=4:
%e ..0..1..0..2..1....1..0..1..1..1....1..0..1..1..2....2..1..2..1..1
%e ..1..2..1..1..0....1..2..1..1..1....1..2..1..1..0....0..1..0..1..1
%e ..1..0..1..1..2....1..0..1..1..1....0..1..0..2..1....1..2..1..2..0
%e ..1..2..1..1..0....1..2..1..1..1....1..2..1..1..0....0..1..0..1..1
%e ..1..0..1..1..2....1..0..1..1..1....0..1..0..2..1....2..1..2..1..1
%Y Column 1 is A048573(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 30 2014