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A206267 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock equal to the number in all its horizontal and vertical neighbors 9
16, 24, 24, 34, 28, 34, 50, 44, 44, 50, 72, 64, 78, 64, 72, 105, 93, 135, 135, 93, 105, 154, 128, 218, 260, 218, 128, 154, 229, 174, 339, 471, 471, 339, 174, 229, 345, 228, 503, 800, 932, 800, 503, 228, 345, 527, 295, 724, 1296, 1725, 1725, 1296, 724, 295, 527, 815, 372 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..16..24..34...50...72...105...154...229...345....527....815...1274...2009

..24..28..44...64...93...128...174...228...295....372....464....568....689

..34..44..78..135..218...339...503...724..1009...1374...1828...2389...3068

..50..64.135..260..471...800..1296..2010..3012...4376...6197...8576..11637

..72..93.218..471..932..1725..3011..5014..8016..12385..18572..27141..38768

.105.128.339..800.1725..3440..6444.11448.19457..31832..50397..77528.116289

.154.174.503.1296.3011..6444.12878.24319.43766..75591.125978.203499.319778

.229.228.724.2010.5014.11448.24319.48628.92387.167968.293939.497428.817199

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..7894

FORMULA

Empirical for column k:

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

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

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

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

k=5: a(n) = 6*a(n-1) -14*a(n-2) +14*a(n-3) -14*a(n-5) +14*a(n-6) -6*a(n-7) +a(n-8) for n>9

k=6: a(n) = 7*a(n-1) -20*a(n-2) +28*a(n-3) -14*a(n-4) -14*a(n-5) +28*a(n-6) -20*a(n-7) +7*a(n-8) -a(n-9) for n>10

k=7: a(n) = 8*a(n-1) -27*a(n-2) +48*a(n-3) -42*a(n-4) +42*a(n-6) -48*a(n-7) +27*a(n-8) -8*a(n-9) +a(n-10) for n>11

EXAMPLE

Some solutions for n=4 k=3

..1..0..0..0....0..0..0..0....1..1..0..0....0..0..1..0....1..0..1..0

..0..0..0..0....0..0..0..0....1..1..0..0....0..1..0..1....0..1..0..1

..0..0..0..0....0..0..0..0....0..0..0..0....1..0..1..0....1..0..1..0

..0..0..0..0....0..0..0..0....0..0..0..0....0..1..0..1....0..1..0..1

..0..0..0..0....0..0..0..0....0..0..0..0....1..0..1..1....1..0..1..1

CROSSREFS

Sequence in context: A166675 A114405 A098351 * A325480 A205193 A052058

Adjacent sequences:  A206264 A206265 A206266 * A206268 A206269 A206270

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Feb 05 2012

STATUS

approved

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Last modified September 22 15:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)