A234140 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9

32, 80, 80, 192, 152, 192, 512, 296, 296, 512, 1280, 680, 488, 680, 1280, 3584, 1544, 968, 968, 1544, 3584, 9216, 4040, 1992, 1640, 1992, 4040, 9216, 26624, 9992, 4808, 2984, 2984, 4808, 9992, 26624, 69632, 28040, 11336, 6440, 4904, 6440, 11336, 28040

Offset

1,1

Comments

Table starts

.....32.....80....192....512...1280...3584...9216..26624...69632..204800

.....80....152....296....680...1544...4040...9992..28040...72200..209672

....192....296....488....968...1992...4808..11336..30536...76872..218696

....512....680....968...1640...2984...6440..14120..35624...86312..236840

...1280...1544...1992...2984...4904...9512..19368..45224..104360..271784

...3584...4040...4808...6440...9512..16424..30632..65192..141224..342440

...9216...9992..11336..14120..19368..30632..53288.104744..214056..481832

..26624..28040..30536..35624..45224..65192.104744.189992..365864..766760

..69632..72200..76872..86312.104360.141224.214056.365864..673832.1338920

.204800.209672.218696.236840.271784.342440.481832.766760.1338920.2532392

Links

R. H. Hardin, Table of n, a(n) for n = 1..480

Formula

Empirical for column k (the same recurrence apparently works on all rows and columns; the k=2 recurrence also works for k=1):

k=1: a(n) = 2*a(n-1) +8*a(n-2) -16*a(n-3)

k=2..7: a(n) = 3*a(n-1) +8*a(n-2) -30*a(n-3) +4*a(n-4) +48*a(n-5) -32*a(n-6)

Example

Some solutions for n=5 k=4
..3..0..0..0..3....0..3..0..3..0....3..2..2..0..3....0..3..2..3..0
..0..0..3..0..0....0..0..0..0..0....2..0..3..2..2....0..0..2..0..0
..3..0..0..0..3....3..0..3..0..3....3..2..2..0..3....0..3..2..3..0
..0..0..3..0..0....2..2..2..2..2....2..0..3..2..2....0..0..2..0..0
..0..3..3..3..0....3..0..3..0..3....3..2..2..0..3....0..3..2..3..0
..0..0..3..0..0....1..1..1..1..1....2..0..3..2..2....2..2..0..2..2

Crossrefs

Sequence in context: A222546 A240054 A135269 * A362044 A086047 A209378

Adjacent sequences: A234137 A234138 A234139 * A234141 A234142 A234143

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2013

Status

approved