A234122 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1

31, 145, 145, 673, 1361, 673, 3127, 12593, 12593, 3127, 14527, 116801, 231713, 116801, 14527, 67489, 1082977, 4279065, 4279065, 1082977, 67489, 313537, 10041953, 79003521, 157630963, 79003521, 10041953, 313537, 1456615, 93113761

Offset

1,1

Comments

Table starts

.......31.........145.............673...............3127.................14527

......145........1361...........12593.............116801...............1082977

......673.......12593..........231713............4279065..............79003521

.....3127......116801.........4279065..........157630963............5807422543

....14527.....1082977........79003521.........5807422543..........427196005695

....67489....10041953......1458813409.......214027901025........31446640848897

...313537....93113761.....26937444801......7888454356625......2315408571668225

..1456615...863396401....497411686793....290756314787875....170502665692732079

..6767071..8005833073...9184935953377..10716964158533127..12556134956123911615

.31438129.74233997105.169604155276817.395017615132720993.924677153131389366689

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +3*a(n-2)

k=2: a(n) = 10*a(n-1) -4*a(n-2) -26*a(n-3) +5*a(n-4)

k=3: a(n) = 20*a(n-1) -10*a(n-2) -324*a(n-3) -277*a(n-4) +144*a(n-5)

k=4: [order 11]

k=5: [order 17]

k=6: [order 35]

k=7: [order 62]

Example

Some solutions for n=2 k=4
..0..1..0..0..1....0..1..2..2..2....1..2..1..2..2....0..1..0..1..2
..1..0..1..0..1....1..1..1..1..2....1..2..2..2..2....1..0..0..1..2
..1..1..0..0..1....1..2..2..1..2....2..1..1..1..2....0..1..0..1..1

Crossrefs

Column 1 is A086901(n+3)

Sequence in context: A185521 A228261 A185513 * A142758 A124994 A126418

Adjacent sequences: A234119 A234120 A234121 * A234123 A234124 A234125

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2013

Status

approved