A206895 Number of nX3 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column or nw-to-se diagonal

62, 3844, 211548, 11745962, 649804846, 35974254384, 1991325229362, 110232229481279, 6102000552869054, 337782083748910144, 18698244855045242630, 1035059000955512487253, 57296667549140793196478

Offset

1,1

Comments

Column 3 of A206900

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 62*a(n-1) -89*a(n-2) -19024*a(n-3) +180385*a(n-4) +1542444*a(n-5) -30585977*a(n-6) +67441748*a(n-7) +1522171819*a(n-8) -10753959118*a(n-9) +884216901*a(n-10) +186281604028*a(n-11) -101724223317*a(n-12) -2245639988086*a(n-13) +1055809482030*a(n-14) +16577430580876*a(n-15) -4024465135169*a(n-16) -81866832640000*a(n-17) +13868518436835*a(n-18) +268430045661884*a(n-19) -66930859905592*a(n-20) -619684819891350*a(n-21) +409676330102717*a(n-22) +861965805151752*a(n-23) -1532757815077997*a(n-24) -219758710136646*a(n-25) +3955755423042556*a(n-26) -3350063434874608*a(n-27) -5839311023587381*a(n-28) +11920153871513458*a(n-29) +1790718602125164*a(n-30) -25047703410910854*a(n-31) +16709018193427569*a(n-32) +30633118950998540*a(n-33) -47761837297486517*a(n-34) -7687101383526230*a(n-35) +67967128227108422*a(n-36) -58912030500691548*a(n-37) -1539628993659391*a(n-38) +41423778208961502*a(n-39) -27897862114690717*a(n-40) -1310209833765998*a(n-41) +9171525316641527*a(n-42) -3560821398329460*a(n-43) +271178518195697*a(n-44) +184523775789700*a(n-45) -190274337478715*a(n-46) +84316407097752*a(n-47) +7655091657948*a(n-48) -14003961247722*a(n-49) +789192911337*a(n-50) +1392712734462*a(n-51) -228397852011*a(n-52) -54902568720*a(n-53) +8399789007*a(n-54) +3008285794*a(n-55) +322041603*a(n-56) -677622236*a(n-57) +126660546*a(n-58) +27470604*a(n-59) -9100699*a(n-60) +40022*a(n-61) -52603*a(n-62) +60398*a(n-63) +2881*a(n-64) -2658*a(n-65) +144*a(n-66)

Example

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

Crossrefs

Sequence in context: A065991 A206833 A206841 * A207285 A042861 A056639

Adjacent sequences: A206892 A206893 A206894 * A206896 A206897 A206898

Keyword

nonn

Author

R. H. Hardin Feb 13 2012

Status

approved