A316300 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

8, 24, 39, 114, 339, 1021, 2929, 8639, 25410, 74617, 219121, 644959, 1895811, 5573758, 16390454, 48201357, 141730361, 416775033, 1225587460, 3603966367, 10597805736, 31164178417, 91641848622, 269483128315, 792446302039

Offset

1,1

Comments

Column 4 of A316304.

Links

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

Formula

Empirical: a(n) = a(n-1) +5*a(n-2) +7*a(n-3) +a(n-4) -28*a(n-5) -34*a(n-6) -44*a(n-7) -53*a(n-8) -31*a(n-9) +137*a(n-10) +472*a(n-11) +460*a(n-12) +290*a(n-13) +212*a(n-14) +30*a(n-15) -967*a(n-16) -1997*a(n-17) -2313*a(n-18) -2769*a(n-19) -2736*a(n-20) -684*a(n-21) +2941*a(n-22) +6131*a(n-23) +8180*a(n-24) +10850*a(n-25) +9043*a(n-26) +2365*a(n-27) -4410*a(n-28) -8926*a(n-29) -15081*a(n-30) -18487*a(n-31) -13111*a(n-32) -4057*a(n-33) +543*a(n-34) +4102*a(n-35) +12555*a(n-36) +17395*a(n-37) +10626*a(n-38) +4523*a(n-39) +2822*a(n-40) +816*a(n-41) -6213*a(n-42) -8546*a(n-43) -4379*a(n-44) -1144*a(n-45) -2219*a(n-46) -2561*a(n-47) +1522*a(n-48) +3387*a(n-49) +1181*a(n-50) -833*a(n-51) -317*a(n-52) +818*a(n-53) +429*a(n-54) -57*a(n-55) -174*a(n-56) -72*a(n-57) +19*a(n-58) +25*a(n-59) +56*a(n-60) -72*a(n-61) -100*a(n-62) -32*a(n-63) +32*a(n-64) +24*a(n-65) for n>67

Example

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

Crossrefs

Cf. A316304.

Sequence in context: A044450 A134223 A304475 * A050427 A329549 A031046

Adjacent sequences: A316297 A316298 A316299 * A316301 A316302 A316303

Keyword

nonn

Author

R. H. Hardin, Jun 29 2018

Status

approved