A297984 Number of nX6 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

1, 53, 14, 43, 61, 131, 242, 530, 1226, 2701, 5847, 13187, 30316, 68963, 156767, 358341, 819778, 1874460, 4286961, 9812357, 22469334, 51467291, 117908386, 270171681, 619170983, 1419191326, 3253216738, 7458029458, 17098984111

Offset

1,2

Comments

Column 6 of A297986.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-3) +22*a(n-4) -34*a(n-5) -3*a(n-6) +77*a(n-7) -115*a(n-8) +109*a(n-9) +59*a(n-10) -221*a(n-11) +337*a(n-12) -190*a(n-13) -235*a(n-14) +367*a(n-15) -673*a(n-16) -171*a(n-17) +413*a(n-18) -454*a(n-19) +515*a(n-20) +1216*a(n-21) +351*a(n-22) +829*a(n-23) +1123*a(n-24) -1315*a(n-25) -1359*a(n-26) -717*a(n-27) -4311*a(n-28) -562*a(n-29) +586*a(n-30) -2822*a(n-31) +4889*a(n-32) +1368*a(n-33) -1161*a(n-34) +5746*a(n-35) -718*a(n-36) +885*a(n-37) +3714*a(n-38) -1567*a(n-39) +3774*a(n-40) +569*a(n-41) -4894*a(n-42) -443*a(n-43) -5804*a(n-44) -7761*a(n-45) -3293*a(n-46) -3623*a(n-47) +690*a(n-48) +4128*a(n-49) +3933*a(n-50) +7042*a(n-51) +5506*a(n-52) +1772*a(n-53) +1624*a(n-54) -1148*a(n-55) -3004*a(n-56) -2143*a(n-57) -2791*a(n-58) -1427*a(n-59) -364*a(n-60) -426*a(n-61) +719*a(n-62) +547*a(n-63) +365*a(n-64) +476*a(n-65) +115*a(n-66) +51*a(n-67) -3*a(n-68) -78*a(n-69) -30*a(n-70) -26*a(n-71) -26*a(n-72) -a(n-73) +2*a(n-75) +2*a(n-76) for n>84

Example

Some solutions for n=7
..0..0..1..1..0..0. .0..0..1..0..1..1. .0..0..1..1..0..0. .0..0..0..0..1..1
..0..1..0..0..1..0. .0..1..1..0..0..1. .0..1..0..0..1..0. .0..1..1..1..0..1
..0..1..1..1..1..0. .1..0..0..1..1..0. .0..1..1..1..1..0. .1..0..0..0..0..1
..1..0..0..0..0..1. .0..1..1..0..0..1. .1..0..0..0..0..1. .0..1..1..1..1..0
..1..0..1..1..1..0. .1..0..0..1..1..0. .0..1..1..1..1..1. .1..0..0..0..0..1
..1..0..1..0..0..1. .0..1..1..0..0..1. .0..0..1..0..0..0. .1..0..1..1..1..0
..1..1..0..0..1..1. .0..0..1..0..1..1. .0..1..1..1..0..1. .1..1..0..0..0..0

Crossrefs

Cf. A297986.

Sequence in context: A143385 A231426 A298061 * A298633 A298710 A048602

Adjacent sequences: A297981 A297982 A297983 * A297985 A297986 A297987

Keyword

nonn

Author

R. H. Hardin, Jan 10 2018

Status

approved