A251326 - OEIS

%I #4 Dec 01 2014 18:56:00

%S 10,28,28,78,116,78,220,474,474,220,618,1982,2804,1982,618,1740,8218,

%T 17216,17216,8218,1740,4894,34288,104058,157312,104058,34288,4894,

%U 13772,142600,636404,1405454,1405454,636404,142600,13772,38746,594236,3866110

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having one or two 1s

%C Table starts

%C .....10.......28........78.........220...........618............1740

%C .....28......116.......474........1982..........8218...........34288

%C .....78......474......2804.......17216........104058..........636404

%C ....220.....1982.....17216......157312.......1405454........12770802

%C ....618.....8218....104058.....1405454......18415674.......246926340

%C ...1740....34288....636404....12770802.....246926340......4911447738

%C ...4894...142600...3866110...114913804....3265612528.....96040080726

%C ..13772...594236..23591052..1040818716...43595364706...1900083059348

%C ..38746..2473510.143559096..9388632290..578517868594..37310824370952

%C .109020.10302766.875140808.84916233072.7707617770032.736337217038262

%H R. H. Hardin, <a href="/A251326/b251326.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)

%F k=2: a(n) = 3*a(n-1) +8*a(n-2) -13*a(n-3) -a(n-4) +2*a(n-5)

%F k=3: [order 10]

%F k=4: [order 19]

%F k=5: [order 36]

%F k=6: [order 71]

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 01 2014