A300317 Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

5, 16, 61, 735, 3486, 25797, 203113, 1378779, 10140973, 75190617, 542109614, 3972097115, 29113049465, 212286481470, 1552987320773, 11358909039391, 83004860334195, 606949455081339, 4437798722528968, 32442321501971416

Offset

1,1

Comments

Column 4 of A300321.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +17*a(n-2) +58*a(n-3) -723*a(n-4) -1474*a(n-5) +2196*a(n-6) +22381*a(n-7) +33196*a(n-8) -74444*a(n-9) -304846*a(n-10) -304618*a(n-11) +729107*a(n-12) +2155348*a(n-13) +1029883*a(n-14) -3952392*a(n-15) -7637046*a(n-16) +715694*a(n-17) +13481890*a(n-18) +8555164*a(n-19) -11449768*a(n-20) -17902612*a(n-21) +4961008*a(n-22) +20105667*a(n-23) +3790762*a(n-24) -14046982*a(n-25) -12943012*a(n-26) +3898385*a(n-27) +15098585*a(n-28) +6519939*a(n-29) -6343052*a(n-30) -9682129*a(n-31) -1312670*a(n-32) +5033072*a(n-33) +1370029*a(n-34) -1279682*a(n-35) -258338*a(n-36) +223424*a(n-37) -7704*a(n-38) -21248*a(n-39) +9856*a(n-40) for n>43

Example

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

Crossrefs

Cf. A300321.

Sequence in context: A189450 A180719 A343164 * A307469 A197549 A365907

Adjacent sequences: A300314 A300315 A300316 * A300318 A300319 A300320

Keyword

nonn

Author

R. H. Hardin, Mar 02 2018

Status

approved