A298255 Number of nX4 0..1 arrays with every element equal to 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 2, 4, 11, 23, 72, 201, 597, 1705, 5141, 15305, 45558, 136366, 408269, 1222895, 3664732, 10990002, 32961810, 98879571, 296674303, 890217834, 2671430941, 8017066909, 24060553805, 72211714389, 216729874503, 650484059608

Offset

1,2

Comments

Column 4 of A298259.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -10*a(n-2) +4*a(n-3) -7*a(n-4) +9*a(n-5) +46*a(n-7) -92*a(n-8) +143*a(n-9) -88*a(n-10) -22*a(n-11) -115*a(n-12) +9*a(n-13) -231*a(n-14) -30*a(n-15) +726*a(n-16) -359*a(n-17) +521*a(n-18) -497*a(n-19) +2917*a(n-20) -2314*a(n-21) -435*a(n-22) +66*a(n-23) -272*a(n-24) -3177*a(n-25) -3089*a(n-26) +4256*a(n-27) +2549*a(n-28) -1942*a(n-29) -1138*a(n-30) +8259*a(n-31) -3970*a(n-32) +431*a(n-33) +2386*a(n-34) -3147*a(n-35) -1866*a(n-36) +196*a(n-37) -83*a(n-38) -673*a(n-39) +507*a(n-40) -882*a(n-41) +1079*a(n-42) +6*a(n-43) +719*a(n-44) -428*a(n-45) +106*a(n-46) -146*a(n-47) +149*a(n-48) -44*a(n-49) -20*a(n-50) -18*a(n-51) +2*a(n-52) +4*a(n-53) for n>54

Example

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

Crossrefs

Cf. A298259.

Sequence in context: A307881 A006452 A104430 * A298926 A292157 A256801

Adjacent sequences: A298252 A298253 A298254 * A298256 A298257 A298258

Keyword

nonn

Author

R. H. Hardin, Jan 15 2018

Status

approved