A317007 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

8, 65, 400, 2567, 16048, 101054, 639838, 4056201, 25720439, 163143336, 1035036752, 6567428128, 41674232746, 264459800134, 1678275645857, 10650595949724, 67590981835505, 428949463478468, 2722231278601382, 17276064752692821

Offset

1,1

Comments

Column 4 of A317011.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -14*a(n-2) +2*a(n-3) -142*a(n-4) +13*a(n-5) +312*a(n-6) +1024*a(n-7) +1722*a(n-8) +599*a(n-9) +178*a(n-10) -16830*a(n-11) -4440*a(n-12) -41055*a(n-13) -71540*a(n-14) +76484*a(n-15) -93690*a(n-16) +406514*a(n-17) +441136*a(n-18) +590146*a(n-19) +621772*a(n-20) +510598*a(n-21) -2981976*a(n-22) +405903*a(n-23) -5317896*a(n-24) -4468266*a(n-25) +1012868*a(n-26) -9416464*a(n-27) +8406357*a(n-28) -2922787*a(n-29) +20775062*a(n-30) +8271486*a(n-31) -7282380*a(n-32) +29780338*a(n-33) -17001742*a(n-34) -34766674*a(n-35) +32742601*a(n-36) -27892831*a(n-37) -6312799*a(n-38) +36022980*a(n-39) -9014846*a(n-40) +65856061*a(n-41) +48095510*a(n-42) -8036671*a(n-43) -29825341*a(n-44) +47705769*a(n-45) -39355385*a(n-46) -23359013*a(n-47) +18658942*a(n-48) -44840756*a(n-49) -9595032*a(n-50) +4859983*a(n-51) -2736914*a(n-52) +1126466*a(n-53) +292506*a(n-54) -1118664*a(n-55) +866208*a(n-56) +611680*a(n-57) for n>59

Example

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

Crossrefs

Cf. A317011.

Sequence in context: A317121 A009373 A305589 * A293802 A316872 A317600

Adjacent sequences: A317004 A317005 A317006 * A317008 A317009 A317010

Keyword

nonn

Author

R. H. Hardin, Jul 18 2018

Status

approved