A205193 T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

16, 24, 24, 48, 40, 48, 72, 64, 64, 72, 144, 104, 124, 104, 144, 216, 168, 160, 160, 168, 216, 432, 272, 292, 256, 292, 272, 432, 648, 440, 384, 384, 384, 384, 440, 648, 1296, 712, 708, 576, 736, 576, 708, 712, 1296, 1944, 1152, 928, 864, 896, 896, 864, 928, 1152

Offset: 1

Author

R. H. Hardin, Jan 23 2012

Keywords

• nonn
• tabl

Comments

Table starts

..16..24..48...72..144..216..432..648..1296..1944..3888..5832.11664.17496.34992

..24..40..64..104..168..272..440..712..1152..1864..3016..4880..7896.12776.20672

..48..64.124..160..292..384..708..928..1708..2240..4124..5408..9956.13056.24036

..72.104.160..256..384..576..864.1312..1984..3008..4544..6880.10400.15744.23808

.144.168.292..384..736..896.1568.1920..3392..4224..7520..9344.16608.20608.36608

.216.272.384..576..896.1408.2048.2944..4224..6144..8960.13184.19328.28416.41600

.432.440.708..864.1568.2048.3904.4608..7872..9216.15808.18944.32960.39936.69824

.648.712.928.1312.1920.2944.4608.7168.10240.14336.19968.28160.39936.57344.82432

Examples

			Some solutions for n=4, k=3
..1..0..0..1....0..1..1..0....1..1..1..0....0..0..1..1....1..1..0..0
..0..1..1..0....0..1..1..1....0..1..1..0....0..0..1..1....1..1..0..0
..1..1..1..0....1..0..1..1....1..0..0..1....1..1..0..0....0..0..1..1
..1..1..0..1....1..1..0..1....0..0..0..1....1..1..0..0....0..0..1..1
..1..0..1..1....1..1..1..0....0..0..1..0....0..0..1..0....1..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1300

Crossrefs

Column 2 is A022091(n+3).

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-2);

k=2: a(n) = a(n-1) +a(n-2);

k=3: a(n) = 2*a(n-2) +a(n-4) for n>5;

k=4: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>6;

k=5: a(n) = 2*a(n-2) +a(n-6) for n>9;

k=6: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) for n>10;

k=7: a(n) = 2*a(n-2) +a(n-8) for n>13;

k=8: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7) +a(n-8) for n>14;

k=9: a(n) = 2*a(n-2) +a(n-10) for n>17;

k=10: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-9) +a(n-10) for n>18;

k=11: a(n) = 2*a(n-2) +a(n-12) for n>21;

k=12: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-9) +a(n-10) -a(n-11) +a(n-12) for n>22;

k=13: a(n) = 2*a(n-2) +a(n-14) for n>25;

k=14: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-9) +a(n-10) -a(n-11) +a(n-12) -a(n-13) +a(n-14) for n>26;

k=15: a(n) = 2*a(n-2) +a(n-16) for n>29;

apparently:

k odd a(n) = 2*a(n-2) +a(n-k-1) for n>2k-1;

k even a(n) = a(n-1) +sum{i in 2..k}(-1^i*a(n-i)) for n>2k-2.