A297872 Number of nX4 0..1 arrays with every element equal to 2, 3 or 5 king-move adjacent elements, with upper left element zero.

0, 2, 3, 10, 20, 68, 185, 561, 1588, 4814, 14322, 42658, 127606, 381695, 1142358, 3419569, 10243325, 30685488, 91937645, 275496007, 825602377, 2474298468, 7415685876, 22226227933, 66617647655, 199673303891, 598488700247

Offset

1,2

Comments

Column 4 of A297876.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -5*a(n-2) -2*a(n-3) -5*a(n-4) +3*a(n-5) +36*a(n-7) -57*a(n-8) +81*a(n-9) +32*a(n-10) -6*a(n-11) -102*a(n-12) -12*a(n-13) -182*a(n-14) -286*a(n-15) +443*a(n-16) -410*a(n-17) +222*a(n-18) -755*a(n-19) +2597*a(n-20) -997*a(n-21) +788*a(n-22) -95*a(n-23) +2600*a(n-24) -2288*a(n-25) -2866*a(n-26) -1124*a(n-27) +2189*a(n-28) -1950*a(n-29) -3437*a(n-30) +2422*a(n-31) +115*a(n-32) +1748*a(n-33) +1283*a(n-34) +1645*a(n-35) +38*a(n-36) +415*a(n-37) -862*a(n-38) +338*a(n-39) -437*a(n-40) -1030*a(n-41) -286*a(n-42) -150*a(n-43) +337*a(n-44) -83*a(n-45) +41*a(n-46) -33*a(n-47) +71*a(n-48) +14*a(n-49) +8*a(n-50) -6*a(n-51) -4*a(n-52) for n>53

Example

Some solutions for n=7
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1
..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..1..0..0. .1..1..0..0. .0..1..0..1. .1..0..1..0. .1..0..0..0
..1..0..1..0. .1..0..1..0. .1..0..0..1. .1..0..1..0. .1..0..1..0
..0..0..1..1. .0..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..1..0
..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..0. .1..0..1..0
..1..1..0..0. .1..1..0..0. .0..0..1..1. .0..0..0..0. .1..1..0..0

Crossrefs

Cf. A297876.

Sequence in context: A148054 A148055 A089791 * A298135 A226356 A141050

Adjacent sequences: A297869 A297870 A297871 * A297873 A297874 A297875

Keyword

nonn

Author

R. H. Hardin, Jan 07 2018

Status

approved