A306139 Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

2, 86, 521, 4691, 40610, 339596, 2880944, 24495738, 207439044, 1759248608, 14920713212, 126511580214, 1072799000264, 9097203457581, 77141534654160, 654142510659999, 5546978690001491, 47037035425953583, 398862931229311745

Offset

1,1

Comments

Column 4 of A306143.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +21*a(n-2) +42*a(n-3) -272*a(n-4) -802*a(n-5) +716*a(n-6) +1254*a(n-7) +1628*a(n-8) +3820*a(n-9) +3392*a(n-10) +5616*a(n-11) -4521*a(n-12) +90544*a(n-13) -83798*a(n-14) -196645*a(n-15) -160167*a(n-16) -340115*a(n-17) +115074*a(n-18) -1571816*a(n-19) +872475*a(n-20) -3665797*a(n-21) +2568784*a(n-22) -4184320*a(n-23) +12824406*a(n-24) +1808033*a(n-25) -14094634*a(n-26) +42149950*a(n-27) -64132166*a(n-28) +94325130*a(n-29) -109401855*a(n-30) +92752488*a(n-31) -37077671*a(n-32) -9295092*a(n-33) -10514542*a(n-34) +36493034*a(n-35) -42516725*a(n-36) +15045839*a(n-37) +1172964*a(n-38) +4753167*a(n-39) -2643483*a(n-40) +1857972*a(n-41) -1874493*a(n-42) +501484*a(n-43) +193967*a(n-44) -364500*a(n-45) +108083*a(n-46) +3620*a(n-47) -10034*a(n-48) +3704*a(n-49) +508*a(n-50) for n>51

Example

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

Crossrefs

Cf. A306143.

Sequence in context: A316579 A304593 A316379 * A317372 A358807 A177318

Adjacent sequences: A306136 A306137 A306138 * A306140 A306141 A306142

Keyword

nonn

Author

R. H. Hardin, Jun 22 2018

Status

approved