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A205193 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor 8
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Column 2 is A022091(n+3)

Sequence in context: A098351 A206267 A325480 * A052058 A105732 A339328

Adjacent sequences:  A205190 A205191 A205192 * A205194 A205195 A205196

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 23 2012

STATUS

approved

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Last modified January 20 08:54 EST 2022. Contains 350471 sequences. (Running on oeis4.)