A297903 Number of nX4 0..1 arrays with every element equal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.

5, 13, 4, 37, 54, 97, 466, 1105, 3354, 12282, 37107, 122676, 416828, 1349661, 4501298, 15041029, 49602808, 165300728, 550279764, 1824434359, 6073061606, 20198360858, 67084559733, 223165737677, 742040901128, 2466100981652, 8201311431601

Offset

1,1

Comments

Column 4 of A297907.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +37*a(n-3) -72*a(n-4) -91*a(n-5) -511*a(n-6) +996*a(n-7) +1127*a(n-8) +3714*a(n-9) -7300*a(n-10) -7764*a(n-11) -16505*a(n-12) +32748*a(n-13) +33291*a(n-14) +48840*a(n-15) -96768*a(n-16) -94276*a(n-17) -101571*a(n-18) +195114*a(n-19) +183178*a(n-20) +153514*a(n-21) -271344*a(n-22) -250136*a(n-23) -171491*a(n-24) +257601*a(n-25) +242029*a(n-26) +141857*a(n-27) -160048*a(n-28) -163417*a(n-29) -85103*a(n-30) +56777*a(n-31) +72364*a(n-32) +33825*a(n-33) -4557*a(n-34) -16800*a(n-35) -5732*a(n-36) -4294*a(n-37) -610*a(n-38) -1765*a(n-39) +1011*a(n-40) +1344*a(n-41) +1068*a(n-42) +241*a(n-43) -214*a(n-44) -147*a(n-45) -78*a(n-46) -4*a(n-47) -2*a(n-48) for n>51

Example

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

Crossrefs

Cf. A297907.

Sequence in context: A088618 A121645 A057691 * A298497 A246922 A246921

Adjacent sequences: A297900 A297901 A297902 * A297904 A297905 A297906

Keyword

nonn

Author

R. H. Hardin, Jan 08 2018

Status

approved