A300111 Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

2, 13, 29, 112, 515, 2713, 12669, 59569, 295903, 1439748, 6946321, 33748534, 164163421, 796809315, 3867558936, 18785049041, 91228838297, 442968357392, 2151023744989, 10445663389464, 50723981600714, 246313304788613

Offset

1,1

Comments

Column 4 of A300115.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -22*a(n-2) +50*a(n-3) -100*a(n-4) +87*a(n-5) -28*a(n-6) +185*a(n-7) -2087*a(n-8) +4007*a(n-9) -1726*a(n-10) +3795*a(n-11) -29105*a(n-12) +114870*a(n-13) -197976*a(n-14) +164388*a(n-15) -38743*a(n-16) +241083*a(n-17) -1477448*a(n-18) +2958415*a(n-19) -3733030*a(n-20) +3976582*a(n-21) -6534750*a(n-22) +11613507*a(n-23) -13103127*a(n-24) +13163030*a(n-25) -16341495*a(n-26) +27407619*a(n-27) -26545990*a(n-28) +6097709*a(n-29) +5793810*a(n-30) -4770508*a(n-31) -1436482*a(n-32) -14106740*a(n-33) +13977469*a(n-34) -5342094*a(n-35) +29552651*a(n-36) -48375324*a(n-37) +47858441*a(n-38) -22810038*a(n-39) +7904052*a(n-40) +2103556*a(n-41) +7347362*a(n-42) -13339150*a(n-43) -10775336*a(n-44) +145017*a(n-45) +10531212*a(n-46) -1184471*a(n-47) -806731*a(n-48) +431595*a(n-49) -409615*a(n-50) +100962*a(n-51) -7225*a(n-52) -27756*a(n-53) +4942*a(n-54) +1168*a(n-55) +38*a(n-56) for n>60

Example

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

Crossrefs

Cf. A300115.

Sequence in context: A298392 A299510 A299310 * A030452 A132602 A359125

Adjacent sequences: A300108 A300109 A300110 * A300112 A300113 A300114

Keyword

nonn

Author

R. H. Hardin, Feb 25 2018

Status

approved