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

Author

R. H. Hardin Sep 21 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A007070

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) [phone]*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) [phone]*a(n-5) -4294967296*a(n-6) for n>9

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