A196861 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,4,2,0,1 for x=0,1,2,3,4

1, 9, 56, 281, 1900, 11280, 62298, 350779, 1995082, 11350977, 64705845, 368982902, 2102619515, 11979490295, 68255053688, 388895058185, 2215852784526, 12625820295021, 71941345568563, 409917070251636, 2335679313403415

Offset

1,2

Comments

Every 0 is next to 0 3's, every 1 is next to 1 4's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 1's

Column 6 of A196863

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -12*a(n-2) +48*a(n-3) -147*a(n-4) +177*a(n-5) -193*a(n-6) +101*a(n-7) -2290*a(n-8) -6713*a(n-9) -8984*a(n-10) +4683*a(n-11) +73021*a(n-12) +144555*a(n-13) +82990*a(n-14) -354364*a(n-15) -821886*a(n-16) -487118*a(n-17) +1188458*a(n-18) +3426796*a(n-19) +4583767*a(n-20) +3457610*a(n-21) -1279713*a(n-22) -10736638*a(n-23) -20765358*a(n-24) -19365134*a(n-25) +5565577*a(n-26) +49807430*a(n-27) +79112975*a(n-28) +42253194*a(n-29) -68005262*a(n-30) -158876744*a(n-31) -98870093*a(n-32) +103621235*a(n-33) +234416864*a(n-34) +107791586*a(n-35) -155468199*a(n-36) -237535086*a(n-37) -42307081*a(n-38) +170054677*a(n-39) +146820334*a(n-40) -31486761*a(n-41) -118923863*a(n-42) -52557457*a(n-43) +34929024*a(n-44) +45892900*a(n-45) +9100577*a(n-46) -15905772*a(n-47) -13411070*a(n-48) +239219*a(n-49) +7571785*a(n-50) +5079825*a(n-51) -253200*a(n-52) -2504227*a(n-53) -2130883*a(n-54) -868904*a(n-55) +278857*a(n-56) +677216*a(n-57) +435396*a(n-58) +76088*a(n-59) -119860*a(n-60) -115074*a(n-61) -29780*a(n-62) +11252*a(n-63) +10748*a(n-64) +3704*a(n-65) +472*a(n-66) -592*a(n-67) -192*a(n-68)

Example

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

Crossrefs

Sequence in context: A212150 A203838 A097556 * A211844 A172065 A002055

Adjacent sequences: A196858 A196859 A196860 * A196862 A196863 A196864

Keyword

nonn

Author

R. H. Hardin Oct 06 2011

Status

approved