A239361 T(n,k)=Number of nXk 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 3

2, 3, 3, 4, 7, 4, 5, 10, 10, 5, 6, 13, 17, 13, 6, 7, 16, 25, 25, 16, 7, 8, 19, 32, 43, 32, 19, 8, 9, 22, 39, 60, 60, 39, 22, 9, 10, 25, 46, 77, 106, 77, 46, 25, 10, 11, 28, 53, 96, 156, 156, 96, 53, 28, 11, 12, 31, 60, 117, 218, 266, 218, 117, 60, 31, 12, 13, 34, 67, 140, 299, 409, 409

Offset

1,1

Comments

Table starts

..2..3..4...5...6....7....8....9....10....11....12....13.....14.....15.....16

..3..7.10..13..16...19...22...25....28....31....34....37.....40.....43.....46

..4.10.17..25..32...39...46...53....60....67....74....81.....88.....95....102

..5.13.25..43..60...77...96..117...140...165...192...221....252....285....320

..6.16.32..60.106..156..218..299...399...524...680...874...1113...1404...1754

..7.19.39..77.156..266..409..599...852..1191..1635..2213...2944...3837...4910

..8.22.46..96.218..409..729.1154..1742..2550..3625..5080...6985...9338..12170

..9.25.53.117.299..599.1154.2151..3568..5605..8500.12681..18578..26346..36540

.10.28.60.140.399..852.1742.3568..7018.12171.19958.32247..50678..76983.114180

.11.31.67.165.524.1191.2550.5605.12171.24408.44086.76871.129200.207531.321665

Links

R. H. Hardin, Table of n, a(n) for n = 1..720

Formula

Empirical for column k:

k=1: a(n) = n + 1

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

k=3: a(n) = 7*n - 3 for n>3

k=4: a(n) = n^2 + 6*n + 5 for n>4

k=5: a(n) = (7/6)*n^3 - (39/2)*n^2 + (538/3)*n - 486 for n>8

k=6: a(n) = (8/3)*n^3 - (45/2)*n^2 + (257/6)*n + 330 for n>13

k=7: a(n) = 7*n^3 - 54*n^2 - 37*n + 1252 for n>16

k=8: a(n) = (1/60)*n^5 + (7/6)*n^4 - (191/12)*n^3 - (1585/6)*n^2 + (107409/10)*n - 83947 for n>19

k=9: a(n) = (17/120)*n^5 + (99/8)*n^4 - (13123/24)*n^3 + (66545/8)*n^2 - (702297/20)*n - 124231 for n>27

k=10: a(n) = (77/60)*n^5 - (23/24)*n^4 + (1018/3)*n^3 - (1527013/24)*n^2 + (104192693/60)*n - 14129021 for n>32

k=11: a(n) = (1/30)*n^6 + (86/15)*n^5 - (2011/24)*n^4 + (48925/12)*n^3 - (48669569/120)*n^2 + (684129941/60)*n - 101487598 for n>37

Example

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

Crossrefs

Sequence in context: A154217 A361644 A185738 * A266362 A241956 A227125

Adjacent sequences: A239358 A239359 A239360 * A239362 A239363 A239364

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 17 2014

Status

approved