A317693 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

5, 21, 33, 141, 630, 2742, 16008, 100830, 603699, 3769795, 24122000, 151848663, 958240276, 6090267864, 38598033209, 244395851672, 1550053828375, 9828877818014, 62296855285711, 394965267640728, 2504248043602690

Offset

1,1

Comments

Column 4 of A317697.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) -51*a(n-2) +199*a(n-3) -1045*a(n-4) +3080*a(n-5) -5824*a(n-6) +19715*a(n-7) -54217*a(n-8) +86631*a(n-9) -208898*a(n-10) +470524*a(n-11) -617540*a(n-12) +1104549*a(n-13) -1778989*a(n-14) +1697347*a(n-15) -2524942*a(n-16) +2404934*a(n-17) -1513005*a(n-18) +185991*a(n-19) +6216357*a(n-20) -6144821*a(n-21) +16299949*a(n-22) -26478742*a(n-23) +17685408*a(n-24) -35457244*a(n-25) +28422411*a(n-26) -13843492*a(n-27) +4891493*a(n-28) -9152979*a(n-29) +11561051*a(n-30) +92789965*a(n-31) +9888284*a(n-32) -76956177*a(n-33) -142623604*a(n-34) -10114987*a(n-35) +126407582*a(n-36) +102361211*a(n-37) -13113374*a(n-38) -92845724*a(n-39) -41282448*a(n-40) +19451206*a(n-41) +23428676*a(n-42) +5104632*a(n-43) -5396697*a(n-44) -2996014*a(n-45) +257192*a(n-46) +493476*a(n-47) +111556*a(n-48) -31808*a(n-49) -14768*a(n-50) +288*a(n-51) +384*a(n-52) for n>55

Example

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

Crossrefs

Cf. A317697.

Sequence in context: A006309 A273577 A317039 * A145026 A039561 A063575

Adjacent sequences: A317690 A317691 A317692 * A317694 A317695 A317696

Keyword

nonn

Author

R. H. Hardin, Aug 04 2018

Status

approved