A298891 Number of nX4 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 2, 4, 11, 31, 80, 229, 681, 1969, 5973, 18031, 54874, 167752, 513625, 1575095, 4835994, 14859480, 45674676, 140452387, 431987865, 1328865560, 4088283165, 12578581331, 38703117525, 119090222855, 366452309799, 1127630050984

Offset

1,2

Comments

Column 4 of A298895.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -9*a(n-2) +5*a(n-3) -32*a(n-4) +38*a(n-5) +25*a(n-6) +98*a(n-7) -119*a(n-8) +40*a(n-9) -550*a(n-10) +580*a(n-11) -916*a(n-12) +830*a(n-13) +263*a(n-14) +83*a(n-15) +2328*a(n-16) -229*a(n-17) +503*a(n-18) -4047*a(n-19) -417*a(n-20) -3044*a(n-21) +2435*a(n-22) -11065*a(n-23) +3356*a(n-24) -5303*a(n-25) +1559*a(n-26) +14545*a(n-27) +32995*a(n-28) +22512*a(n-29) -15204*a(n-30) -12820*a(n-31) -31577*a(n-32) -21644*a(n-33) +3315*a(n-34) +18307*a(n-35) -24537*a(n-36) -14373*a(n-37) +11731*a(n-38) +26599*a(n-39) +15792*a(n-40) -11544*a(n-41) -3386*a(n-42) -4977*a(n-43) +5179*a(n-44) -2851*a(n-45) +4056*a(n-46) -977*a(n-47) +3855*a(n-48) -121*a(n-49) +305*a(n-50) -1567*a(n-51) -458*a(n-52) -273*a(n-53) +321*a(n-54) -8*a(n-55) +78*a(n-56) -20*a(n-57) -6*a(n-58) for n>59

Example

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

Crossrefs

Cf. A298895.

Sequence in context: A193059 A034770 A276687 * A002387 A325922 A148160

Adjacent sequences: A298888 A298889 A298890 * A298892 A298893 A298894

Keyword

nonn

Author

R. H. Hardin, Jan 28 2018

Status

approved