A240422 T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4

3, 7, 7, 15, 35, 15, 31, 147, 147, 31, 63, 553, 1161, 553, 63, 127, 2045, 7857, 7857, 2045, 127, 255, 7439, 52711, 97269, 52711, 7439, 255, 511, 27099, 347155, 1197511, 1197511, 347155, 27099, 511, 1023, 98193, 2331517, 14516959, 27488435, 14516959

Offset

1,1

Comments

Table starts

....3.......7........15..........31...........63...........127...........255

....7......35.......147.........553.........2045..........7439.........27099

...15.....147......1161........7857........52711........347155.......2331517

...31.....553......7857.......97269......1197511......14516959.....182716785

...63....2045.....52711.....1197511.....27488435.....619040901...14838256141

..127....7439....347155....14516959....619040901...26075879845.1191246174665

..255...27099...2331517...182716785..14838256141.1191246174665

..511...98193..15537761..2283795777.349768244657

.1023..356367.105095051.29455167803

.2047.1290555.706172043

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

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

k=2: [order 15]

k=3: [order 96] for n>100

Example

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

Crossrefs

Column 1 is A000225(n+1)

Sequence in context: A059478 A175329 A081218 * A130003 A098581 A238997

Adjacent sequences: A240419 A240420 A240421 * A240423 A240424 A240425

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved