A305645 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

5, 21, 31, 137, 574, 2360, 13498, 83190, 481377, 2919477, 18188505, 111190231, 681420231, 4209030021, 25916430566, 159406198332, 982241553059, 6051046080917, 37258819107772, 229490403681192, 1413605674151764

Offset

1,1

Comments

Column 4 of A305649.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) -53*a(n-2) +208*a(n-3) -1025*a(n-4) +3124*a(n-5) -6614*a(n-6) +20019*a(n-7) -52896*a(n-8) +95825*a(n-9) -213582*a(n-10) +452071*a(n-11) -722917*a(n-12) +1317805*a(n-13) -2044503*a(n-14) +2703274*a(n-15) -4185687*a(n-16) +4037722*a(n-17) -3566939*a(n-18) +2631534*a(n-19) +6295616*a(n-20) -11042762*a(n-21) +24218324*a(n-22) -54093882*a(n-23) +63608167*a(n-24) -77176201*a(n-25) +118700537*a(n-26) -166637364*a(n-27) +138057125*a(n-28) -110211186*a(n-29) +164465821*a(n-30) -107581221*a(n-31) +147189359*a(n-32) -69901128*a(n-33) -233098157*a(n-34) +37858384*a(n-35) +6891596*a(n-36) +250149252*a(n-37) -131157175*a(n-38) +122684063*a(n-39) -39643231*a(n-40) -101368179*a(n-41) -102287871*a(n-42) -94827300*a(n-43) +50798280*a(n-44) +27596612*a(n-45) +23871896*a(n-46) +11304776*a(n-47) +4047152*a(n-48) +902752*a(n-49) -175152*a(n-50) +240928*a(n-51) -119104*a(n-52) +7552*a(n-53) +2560*a(n-54) for n>57

Example

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

Crossrefs

Cf. A305649.

Sequence in context: A317156 A304665 A306168 * A316921 A316423 A317425

Adjacent sequences: A305642 A305643 A305644 * A305646 A305647 A305648

Keyword

nonn

Author

R. H. Hardin, Jun 07 2018

Status

approved