A318419 Number of nX4 0..1 arrays with every element unequal to 0, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 3, 4, 18, 71, 126, 225, 691, 2116, 6101, 15907, 40782, 110244, 304223, 831408, 2242597, 6029313, 16289354, 44168735, 119711796, 323891119, 875720673, 2368763705, 6410688069, 17350642443, 46950362332, 127030237584, 343705347091

Offset

1,2

Comments

Column 4 of A318423.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) +4*a(n-4) +16*a(n-5) -54*a(n-6) -33*a(n-7) -5*a(n-8) +65*a(n-9) -60*a(n-10) +347*a(n-11) +500*a(n-12) +18*a(n-13) -1273*a(n-14) -1375*a(n-15) -535*a(n-16) +1263*a(n-17) +1915*a(n-18) +2355*a(n-19) +1295*a(n-20) -1376*a(n-21) -3566*a(n-22) -5004*a(n-23) +351*a(n-24) +75*a(n-25) +6701*a(n-26) +2472*a(n-27) +1912*a(n-28) -2283*a(n-29) -3175*a(n-30) -1585*a(n-31) -5971*a(n-32) +6954*a(n-33) -3473*a(n-34) +8526*a(n-35) -7781*a(n-36) +7422*a(n-37) -7217*a(n-38) +5602*a(n-39) -6347*a(n-40) +5010*a(n-41) -2648*a(n-42) +1948*a(n-43) -1693*a(n-44) +948*a(n-45) -461*a(n-46) +195*a(n-47) +168*a(n-48) -246*a(n-49) +183*a(n-50) -93*a(n-51) -4*a(n-52) +13*a(n-53) -13*a(n-54) +22*a(n-55) -14*a(n-56) +5*a(n-57) -a(n-58) for n>62

Example

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

Crossrefs

Cf. A318423.

Sequence in context: A222691 A254201 A222795 * A263968 A020344 A344459

Adjacent sequences: A318416 A318417 A318418 * A318420 A318421 A318422

Keyword

nonn

Author

R. H. Hardin, Aug 26 2018

Status

approved