A317234 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

8, 24, 60, 168, 674, 2432, 8255, 29245, 105103, 371011, 1309368, 4655316, 16519210, 58492609, 207432479, 735833616, 2608622433, 9248841123, 32798084620, 116297139395, 412355808249, 1462162440452, 5184649702920, 18383824165115

Offset

1,1

Comments

Column 4 of A317238.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -30*a(n-4) -105*a(n-5) -90*a(n-6) +243*a(n-7) +519*a(n-8) +69*a(n-9) -377*a(n-10) +294*a(n-11) +118*a(n-12) -3127*a(n-13) -3198*a(n-14) +2938*a(n-15) +4164*a(n-16) -2745*a(n-17) -4385*a(n-18) +8169*a(n-19) +6852*a(n-20) -8746*a(n-21) +621*a(n-22) +29311*a(n-23) +38056*a(n-24) -3386*a(n-25) -27694*a(n-26) -38080*a(n-27) -52553*a(n-28) -66971*a(n-29) -20347*a(n-30) +7680*a(n-31) -16042*a(n-32) -10748*a(n-33) +50135*a(n-34) +71155*a(n-35) +74550*a(n-36) +91045*a(n-37) +80291*a(n-38) +34495*a(n-39) +5003*a(n-40) -35815*a(n-41) -82100*a(n-42) -76688*a(n-43) -51319*a(n-44) -35830*a(n-45) -2754*a(n-46) +40983*a(n-47) +33705*a(n-48) +3308*a(n-49) -7293*a(n-50) -3707*a(n-51) -2336*a(n-52) +2858*a(n-53) +5853*a(n-54) +1546*a(n-55) -1048*a(n-56) +133*a(n-57) +540*a(n-58) -801*a(n-59) -792*a(n-60) -190*a(n-61) +18*a(n-62) +4*a(n-63) +52*a(n-64) +48*a(n-65) for n>67

Example

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

Crossrefs

Cf. A317238.

Sequence in context: A129959 A256533 A177719 * A049724 A060602 A066605

Adjacent sequences: A317231 A317232 A317233 * A317235 A317236 A317237

Keyword

nonn

Author

R. H. Hardin, Jul 24 2018

Status

approved