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A241306 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4 12
2, 2, 5, 4, 6, 11, 6, 15, 6, 25, 8, 25, 37, 12, 57, 14, 40, 74, 116, 16, 129, 20, 89, 186, 330, 304, 28, 293, 30, 121, 646, 1462, 1145, 869, 38, 665, 48, 237, 1278, 5757, 6718, 4499, 2398, 66, 1509, 70, 390, 3418, 22343, 49918, 41336, 15827, 6813, 92, 3425, 108, 682 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....2...2.....4......6........8.........14..........20..........30..........48

....5...6....15.....25.......40.........89.........121.........237.........390

...11...6....37.....74......186........646........1278........3418........9113

...25..12...116....330.....1462.......5757.......22343.......79043......304799

...57..16...304...1145.....6718......49918......283985.....1666242.....9581018

..129..28...869...4499....41336.....490486.....5098814....41458261...447396605

..293..38..2398..15827...217785....3893262....70316883...978925384.16677156613

..665..66..6813..58043..1215485...37039909..1194164944.30759996872

.1509..92.18782.209838..6526016..307030328.16586413847

.3425.154.53067.757771.35833494.2801405991

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..126

FORMULA

Empirical for column k:

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

k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5)

Empirical for row n:

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

n=2: [order 14] for n>20

EXAMPLE

Some solutions for n=4 k=4

..3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..2....3..2..2..2

..1..2..1..1....3..1..3..1....1..2..1..1....1..2..1..1....3..0..0..1

..2..0..0..1....1..2..2..3....3..2..2..2....3..2..0..2....1..0..2..1

..1..0..3..3....2..0..0..1....1..2..0..2....2..0..0..3....1..0..0..2

CROSSREFS

Column 1 is A239812

Row 1 is A239851

Sequence in context: A284127 A261114 A284827 * A336073 A266792 A162200

Adjacent sequences:  A241303 A241304 A241305 * A241307 A241308 A241309

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 18 2014

STATUS

approved

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Last modified August 3 10:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)