A300142 Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 16, 18, 246, 1043, 5368, 37739, 219689, 1245482, 7870135, 47636355, 282097766, 1725080678, 10469667595, 62941560035, 381690476085, 2313274299430, 13972436055633, 84576042864758, 512096642082119, 3097315708720487

Offset

1,2

Comments

Column 4 of A300146.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +10*a(n-2) +90*a(n-3) -294*a(n-4) -1000*a(n-5) -1788*a(n-6) +8408*a(n-7) +19306*a(n-8) +13989*a(n-9) -82811*a(n-10) -186056*a(n-11) -11348*a(n-12) +460563*a(n-13) +742483*a(n-14) -281458*a(n-15) -1785439*a(n-16) -836008*a(n-17) +2523733*a(n-18) +1976018*a(n-19) -2319096*a(n-20) -2899510*a(n-21) +899133*a(n-22) +4429039*a(n-23) -1751184*a(n-24) -2174228*a(n-25) +1243411*a(n-26) -1154919*a(n-27) +1558675*a(n-28) +108867*a(n-29) -1129196*a(n-30) +676303*a(n-31) +410519*a(n-32) +172464*a(n-33) -226281*a(n-34) -319702*a(n-35) +87836*a(n-36) +54124*a(n-37) -16318*a(n-38) -2084*a(n-39) +1232*a(n-40) for n>42

Example

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

Crossrefs

Cf. A300146.

Sequence in context: A223588 A358423 A183401 * A070574 A249612 A260560

Adjacent sequences: A300139 A300140 A300141 * A300143 A300144 A300145

Keyword

nonn

Author

R. H. Hardin, Feb 26 2018

Status

approved