A305093 Number of nX4 0..1 arrays with every element unequal to 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

2, 10, 17, 20, 37, 142, 295, 459, 1201, 3140, 5679, 11961, 30760, 65672, 131365, 307549, 703252, 1466918, 3214273, 7362021, 16026098, 34540558, 77372285, 171866728, 373246320, 822381926, 1829780399, 4016363100, 8804567379

Offset

1,1

Comments

Column 4 of A305097.

Links

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +8*a(n-3) -5*a(n-4) -41*a(n-5) -51*a(n-6) +18*a(n-7) +129*a(n-8) +150*a(n-9) +84*a(n-10) +28*a(n-11) -181*a(n-12) -565*a(n-13) -531*a(n-14) +108*a(n-15) +151*a(n-16) -535*a(n-17) +219*a(n-18) +2126*a(n-19) +2203*a(n-20) -1637*a(n-21) -1492*a(n-22) +1388*a(n-23) +2081*a(n-24) +3836*a(n-25) +4471*a(n-26) +4944*a(n-27) -15416*a(n-28) -19801*a(n-29) -10113*a(n-30) -9394*a(n-31) +7*a(n-32) +3731*a(n-33) +13760*a(n-34) -10419*a(n-35) +27310*a(n-36) +52883*a(n-37) +22041*a(n-38) -6115*a(n-39) -809*a(n-40) +20488*a(n-41) -42320*a(n-42) -30422*a(n-43) -9010*a(n-44) -3526*a(n-45) -15159*a(n-46) -9972*a(n-47) +20205*a(n-48) +2987*a(n-49) +3492*a(n-50) -6258*a(n-51) +373*a(n-52) -7508*a(n-53) +1019*a(n-54) +6434*a(n-55) +4843*a(n-56) +2977*a(n-57) +1648*a(n-58) +1235*a(n-59) -1177*a(n-60) -1220*a(n-61) -998*a(n-62) -406*a(n-63) -95*a(n-64) +46*a(n-65) +67*a(n-66) +28*a(n-67) +28*a(n-68) +15*a(n-69) +3*a(n-70) -4*a(n-71) for n>72

Example

Some solutions for n=5
..0..0..0..1. .0..0..0..0. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..1..1..1. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..1..1
..1..0..0..1. .0..0..0..0. .1..1..1..1. .0..0..0..0. .0..1..1..1
..1..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..0..0..0. .0..0..0..0. .0..1..0..1. .0..1..0..1. .1..1..1..0

Crossrefs

Cf. A305097.

Sequence in context: A276046 A268481 A009387 * A316753 A304809 A304805

Adjacent sequences: A305090 A305091 A305092 * A305094 A305095 A305096

Keyword

nonn

Author

R. H. Hardin, May 25 2018

Status

approved