A304540 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

5, 17, 19, 70, 124, 328, 808, 2265, 6025, 17221, 50786, 150521, 450244, 1372877, 4203380, 12926183, 39917505, 123702709, 384029038, 1194002908, 3716951098, 11582357384, 36113695489, 112659146087, 351593620707, 1097602370102

Offset

1,1

Comments

Column 4 of A304544.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -25*a(n-2) +49*a(n-3) -88*a(n-4) +119*a(n-5) -65*a(n-6) -152*a(n-7) +613*a(n-8) -1383*a(n-9) +2833*a(n-10) -3476*a(n-11) +1201*a(n-12) +2494*a(n-13) -6327*a(n-14) +5441*a(n-15) -2980*a(n-16) -13831*a(n-17) +51108*a(n-18) -53298*a(n-19) +43112*a(n-20) -28850*a(n-21) +9006*a(n-22) +15154*a(n-23) -86293*a(n-24) -173782*a(n-25) +97622*a(n-26) +351116*a(n-27) +771915*a(n-28) -1045721*a(n-29) +1602347*a(n-30) -1101590*a(n-31) -2933350*a(n-32) +2498594*a(n-33) -7951102*a(n-34) +7535499*a(n-35) -364183*a(n-36) +900547*a(n-37) +7133262*a(n-38) -9043595*a(n-39) +18595484*a(n-40) -12396661*a(n-41) +1055632*a(n-42) -5204833*a(n-43) -9274042*a(n-44) +4026235*a(n-45) -15979781*a(n-46) +18245073*a(n-47) +1039538*a(n-48) +9218669*a(n-49) -7253444*a(n-50) +738543*a(n-51) -21115*a(n-52) +1181762*a(n-53) -1020586*a(n-54) -1433205*a(n-55) -247891*a(n-56) +220792*a(n-57) +190608*a(n-58) -115798*a(n-59) +59808*a(n-60) +51680*a(n-61) +12336*a(n-62) -10128*a(n-63) +128*a(n-64) -3264*a(n-65) -384*a(n-66) +256*a(n-67) for n>68

Example

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

Crossrefs

Cf. A304544.

Sequence in context: A171253 A226623 A171255 * A306125 A255901 A098333

Adjacent sequences: A304537 A304538 A304539 * A304541 A304542 A304543

Keyword

nonn

Author

R. H. Hardin, May 14 2018

Status

approved