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

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

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