A229392 T(n,k)=Number of nXk 0..3 arrays of the sum of the corresponding element, the element to the east and the element to the south in a larger (n+1)X(k+1) 0..1 array

4, 14, 14, 48, 128, 48, 164, 1064, 1064, 164, 560, 8592, 19124, 8592, 560, 1912, 68672, 319340, 319340, 68672, 1912, 6528, 546752, 5212236, 10624396, 5212236, 546752, 6528, 22288, 4346752, 84210828, 345788172, 345788172, 84210828, 4346752, 22288

Offset

1,1

Comments

Table starts

.....4........14...........48.............164................560

....14.......128.........1064............8592..............68672

....48......1064........19124..........319340............5212236

...164......8592.......319340........10624396..........345788172

...560.....68672......5212236.......345788172........22494002188

..1912....546752.....84210828.....11156280332......1451228983308

..6528...4346752...1353901580....358453456908.....93250181644300

.22288..34537984..21715025932..11493734735884...5979900142878732

.76096.274370048.347864379404.368171037655052.383094040360124428

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

k=2: a(n) = 12*a(n-1) -36*a(n-2) +32*a(n-3) -16*a(n-4)

k=3: a(n) = 25*a(n-1) -152*a(n-2) +144*a(n-3) -368*a(n-4) +1888*a(n-5) -1536*a(n-6) for n>9

k=4: a(n) = 49*a(n-1) -560*a(n-2) +544*a(n-3) -1568*a(n-4) +17920*a(n-5) -16384*a(n-6) for n>9

k=5: a(n) = 101*a(n-1) -2532*a(n-2) +10624*a(n-3) -8192*a(n-4) for n>7

k=6: a(n) = 193*a(n-1) -8384*a(n-2) +8320*a(n-3) -24704*a(n-4) +1073152*a(n-5) -1048576*a(n-6) for n>9

k=7: a(n) = 385*a(n-1) -33152*a(n-2) +33024*a(n-3) -98560*a(n-4) +8486912*a(n-5) -8388608*a(n-6) for n>9

k=8: a(n) = 777*a(n-1) -137992*a(n-2) +1185792*a(n-3) -1048576*a(n-4) for n>7

k=9: a(n) = 1537*a(n-1) -525824*a(n-2) +525312*a(n-3) -1573888*a(n-4) +538443776*a(n-5) -536870912*a(n-6) for n>9

k=10: a(n) = 3073*a(n-1) -2100224*a(n-2) +2099200*a(n-3) -6293504*a(n-4) +4301258752*a(n-5) -4294967296*a(n-6) for n>9

k=11: a(n) = 6161*a(n-1) -8493072*a(n-2) +142704640*a(n-3) -134217728*a(n-4) for n>7

Example

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

Crossrefs

Column 1 is A007070

Sequence in context: A168420 A189814 A200553 * A229320 A127302 A204541

Adjacent sequences: A229389 A229390 A229391 * A229393 A229394 A229395

Keyword

nonn,tabl

Author

R. H. Hardin Sep 21 2013

Status

approved