A304955 Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

2, 45, 118, 496, 2080, 8361, 35441, 148491, 621640, 2614631, 10980051, 46108520, 193777385, 814071188, 3420213425, 14370988671, 60379626904, 253690644748, 1065913057859, 4478525703364, 18817002121087, 79061634858065

Offset

1,1

Comments

Column 4 of A304959.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +5*a(n-2) +26*a(n-3) -71*a(n-4) -125*a(n-5) -323*a(n-6) +458*a(n-7) +975*a(n-8) +1918*a(n-9) -70*a(n-10) -1197*a(n-11) -3025*a(n-12) -1281*a(n-13) -4758*a(n-14) -7839*a(n-15) -10463*a(n-16) -38528*a(n-17) -40971*a(n-18) -139418*a(n-19) -49009*a(n-20) +37502*a(n-21) +410850*a(n-22) +1145184*a(n-23) +1501460*a(n-24) +1924001*a(n-25) +604450*a(n-26) -1245485*a(n-27) -3285482*a(n-28) -5607549*a(n-29) -6117526*a(n-30) -7515067*a(n-31) -6020827*a(n-32) -2387648*a(n-33) +1374890*a(n-34) +5596571*a(n-35) +6885885*a(n-36) +7947766*a(n-37) +9619088*a(n-38) +10500451*a(n-39) +7379338*a(n-40) +4822110*a(n-41) +1762915*a(n-42) -628945*a(n-43) +2651452*a(n-44) +1467499*a(n-45) +174173*a(n-46) +300100*a(n-47) -1711642*a(n-48) -540748*a(n-49) +958090*a(n-50) -8087*a(n-51) -404816*a(n-52) +291351*a(n-53) -124343*a(n-54) -37128*a(n-55) +205244*a(n-56) -163174*a(n-57) +27184*a(n-58) +55353*a(n-59) -51052*a(n-60) +13942*a(n-61) +2972*a(n-62) -10778*a(n-63) +294*a(n-64) +812*a(n-65) -380*a(n-66) +92*a(n-67) +168*a(n-68) +32*a(n-69) for n>71

Example

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

Crossrefs

Cf. A304959.

Sequence in context: A304015 A279680 A305363 * A316637 A281661 A019579

Adjacent sequences: A304952 A304953 A304954 * A304956 A304957 A304958

Keyword

nonn

Author

R. H. Hardin, May 22 2018

Status

approved