|
%I #4 Mar 17 2014 06:39:10
%S 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,
%T 8,9,22,39,60,60,39,22,9,10,25,46,77,106,77,46,25,10,11,28,53,96,156,
%U 156,96,53,28,11,12,31,60,117,218,266,218,117,60,31,12,13,34,67,140,299,409,409
%N 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
%C Table starts
%C ..2..3..4...5...6....7....8....9....10....11....12....13.....14.....15.....16
%C ..3..7.10..13..16...19...22...25....28....31....34....37.....40.....43.....46
%C ..4.10.17..25..32...39...46...53....60....67....74....81.....88.....95....102
%C ..5.13.25..43..60...77...96..117...140...165...192...221....252....285....320
%C ..6.16.32..60.106..156..218..299...399...524...680...874...1113...1404...1754
%C ..7.19.39..77.156..266..409..599...852..1191..1635..2213...2944...3837...4910
%C ..8.22.46..96.218..409..729.1154..1742..2550..3625..5080...6985...9338..12170
%C ..9.25.53.117.299..599.1154.2151..3568..5605..8500.12681..18578..26346..36540
%C .10.28.60.140.399..852.1742.3568..7018.12171.19958.32247..50678..76983.114180
%C .11.31.67.165.524.1191.2550.5605.12171.24408.44086.76871.129200.207531.321665
%H R. H. Hardin, <a href="/A239361/b239361.txt">Table of n, a(n) for n = 1..720</a>
%F Empirical for column k:
%F k=1: a(n) = n + 1
%F k=2: a(n) = 3*n + 1 for n>1
%F k=3: a(n) = 7*n - 3 for n>3
%F k=4: a(n) = n^2 + 6*n + 5 for n>4
%F k=5: a(n) = (7/6)*n^3 - (39/2)*n^2 + (538/3)*n - 486 for n>8
%F k=6: a(n) = (8/3)*n^3 - (45/2)*n^2 + (257/6)*n + 330 for n>13
%F k=7: a(n) = 7*n^3 - 54*n^2 - 37*n + 1252 for n>16
%F 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
%F 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
%F 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
%F 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
%e Some solutions for n=5 k=4
%e ..0..0..0..0....0..0..0..0....0..0..0..2....0..0..0..2....0..0..0..0
%e ..0..0..0..0....0..0..0..2....0..0..2..2....0..0..0..2....0..0..0..2
%e ..0..0..0..2....0..0..0..2....0..0..2..1....0..0..0..0....0..0..2..2
%e ..0..0..2..2....0..0..0..0....2..2..0..1....0..0..0..0....0..0..2..1
%e ..0..0..2..1....0..0..0..0....2..2..1..2....2..2..0..0....0..0..0..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 17 2014
| 