A300085 Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

5, 8, 4, 25, 50, 98, 359, 766, 1932, 5677, 12860, 34902, 92923, 224468, 609898, 1569799, 3969016, 10617506, 27213371, 70541934, 186417464, 481204483, 1261639106, 3316784004, 8641317351, 22770348996, 59873020940, 157234586213

Offset

1,1

Comments

Column 4 of A300089.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +a(n-2) +23*a(n-3) -77*a(n-4) +5*a(n-5) -303*a(n-6) +735*a(n-7) -169*a(n-8) +2494*a(n-9) -3571*a(n-10) +1775*a(n-11) -10599*a(n-12) +9687*a(n-13) -8801*a(n-14) +23592*a(n-15) -19900*a(n-16) +18698*a(n-17) -34363*a(n-18) +29869*a(n-19) -21710*a(n-20) +36339*a(n-21) -31007*a(n-22) +16036*a(n-23) -26673*a(n-24) +26280*a(n-25) -4804*a(n-26) +15200*a(n-27) -19964*a(n-28) -4002*a(n-29) -9745*a(n-30) +12193*a(n-31) +4104*a(n-32) +5170*a(n-33) -7137*a(n-34) -2131*a(n-35) -834*a(n-36) +4727*a(n-37) +2072*a(n-38) -544*a(n-39) -2800*a(n-40) -1833*a(n-41) +287*a(n-42) +1272*a(n-43) +1184*a(n-44) -38*a(n-45) -361*a(n-46) -569*a(n-47) -23*a(n-48) +69*a(n-49) +172*a(n-50) +27*a(n-51) -23*a(n-52) -34*a(n-53) -10*a(n-54) +5*a(n-55) +7*a(n-56) +a(n-57) -a(n-59) for n>61

Example

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

Crossrefs

Cf. A300089.

Sequence in context: A334116 A222591 A299447 * A186691 A199057 A090550

Adjacent sequences: A300082 A300083 A300084 * A300086 A300087 A300088

Keyword

nonn

Author

R. H. Hardin, Feb 24 2018

Status

approved