

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


5



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
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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: A078467 A154217 A185738 * A266362 A241956 A227125
Adjacent sequences: A239358 A239359 A239360 * A239362 A239363 A239364


KEYWORD

nonn,tabl


AUTHOR

R. H. Hardin, Mar 17 2014


STATUS

approved



