A306125 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

5, 17, 19, 70, 134, 360, 964, 2805, 8207, 24747, 77226, 241685, 759584, 2416011, 7719948, 24722213, 79338163, 255258059, 822455126, 2651969050, 8558214320, 27638113884, 89293362591, 288580383107, 932903497169, 3016487687932

Offset

1,1

Comments

Column 4 of A306129.

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) +50*a(n-3) -91*a(n-4) +124*a(n-5) -120*a(n-6) +111*a(n-7) -117*a(n-8) -57*a(n-9) +1422*a(n-10) -2842*a(n-11) +2995*a(n-12) -4038*a(n-13) +6271*a(n-14) -7029*a(n-15) -1871*a(n-16) -15749*a(n-17) +45068*a(n-18) -29238*a(n-19) -11829*a(n-20) -13467*a(n-21) +121211*a(n-22) +105023*a(n-23) -109380*a(n-24) -364968*a(n-25) +909532*a(n-26) -489713*a(n-27) +105583*a(n-28) -1369411*a(n-29) +1850541*a(n-30) -420304*a(n-31) -5805132*a(n-32) +497842*a(n-33) -3558245*a(n-34) +6905661*a(n-35) +1832173*a(n-36) +5566908*a(n-37) +19899549*a(n-38) -9420347*a(n-39) +14803578*a(n-40) -7946936*a(n-41) -11244317*a(n-42) -1408955*a(n-43) -30465026*a(n-44) -6249506*a(n-45) -34375368*a(n-46) +817988*a(n-47) +14972721*a(n-48) +9589036*a(n-49) +20715181*a(n-50) +4441849*a(n-51) +12903307*a(n-52) -5950420*a(n-53) +252652*a(n-54) -4307590*a(n-55) -1421094*a(n-56) -1915678*a(n-57) -919320*a(n-58) +228232*a(n-59) +276920*a(n-60) +280520*a(n-61) -18928*a(n-62) +26896*a(n-63) -3936*a(n-64) -3264*a(n-65) -1152*a(n-66) +256*a(n-67) for n>68

Example

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

Crossrefs

Cf. A306129.

Sequence in context: A226623 A171255 A304540 * A255901 A098333 A252232

Adjacent sequences: A306122 A306123 A306124 * A306126 A306127 A306128

Keyword

nonn

Author

R. H. Hardin, Jun 22 2018

Status

approved