A298164 Number of n X 5 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 3, 3, 6, 10, 18, 32, 80, 171, 528, 1439, 4889, 15449, 53949, 182180, 637755, 2204512, 7715118, 26867102, 93989058, 328149079, 1147549260, 4010085072, 14021225991, 49011288024, 171356237471, 599040489814, 2094336965494, 7321826414980

Offset

1,2

Comments

Column 5 of A298167.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +11*a(n-2) -23*a(n-3) -63*a(n-4) +38*a(n-5) +294*a(n-6) +37*a(n-7) -1002*a(n-8) +36*a(n-9) +2280*a(n-10) -608*a(n-11) -3730*a(n-12) +119*a(n-13) +5320*a(n-14) +4302*a(n-15) -7171*a(n-16) -13410*a(n-17) +6800*a(n-18) +28234*a(n-19) +815*a(n-20) -54073*a(n-21) -10366*a(n-22) +86948*a(n-23) +4709*a(n-24) -108386*a(n-25) +16156*a(n-26) +116955*a(n-27) -33161*a(n-28) -124987*a(n-29) +40940*a(n-30) +132629*a(n-31) -62606*a(n-32) -115911*a(n-33) +95342*a(n-34) +85712*a(n-35) -144819*a(n-36) -105111*a(n-37) +216302*a(n-38) +160234*a(n-39) -200504*a(n-40) -180984*a(n-41) +8541*a(n-42) +224078*a(n-43) +219299*a(n-44) -322041*a(n-45) -229238*a(n-46) +296497*a(n-47) +68426*a(n-48) -149490*a(n-49) +38540*a(n-50) +21468*a(n-51) -25611*a(n-52) +28803*a(n-53) -9090*a(n-54) -6735*a(n-55) +1864*a(n-56) -1716*a(n-57) +2058*a(n-58) -1281*a(n-59) -1710*a(n-60) -102*a(n-61) +264*a(n-62) -12*a(n-63) -100*a(n-64) +20*a(n-65) +28*a(n-66) +4*a(n-67).

Example

Some solutions for n=8
..0..0..0..1..1. .0..0..0..0..0. .0..0..0..1..1. .0..0..0..1..1
..0..0..0..1..1. .0..0..1..0..0. .0..0..0..1..1. .0..0..0..1..1
..0..0..0..1..1. .1..1..1..1..0. .0..0..0..1..1. .1..1..1..0..0
..0..0..0..1..1. .1..1..0..0..1. .0..0..0..1..1. .1..1..1..0..0
..0..0..0..1..1. .1..0..0..1..1. .0..0..0..1..1. .0..0..0..1..1
..1..1..1..0..0. .0..1..1..1..1. .0..0..0..1..1. .0..0..0..1..1
..1..1..1..0..0. .0..0..1..0..0. .0..0..0..1..1. .1..1..1..0..0
..1..1..1..0..0. .0..0..0..0..0. .0..0..0..1..1. .1..1..1..0..0

Crossrefs

Cf. A298167.

Sequence in context: A366317 A300301 A031504 * A304265 A049871 A049924

Adjacent sequences: A298161 A298162 A298163 * A298165 A298166 A298167

Keyword

nonn

Author

R. H. Hardin, Jan 14 2018

Status

approved