A297946 Number of nX3 0..1 arrays with every element equal to 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 18, 56, 219, 796, 3079, 11614, 44076, 167210, 635033, 2409994, 9147953, 34722997, 131802284, 500289672, 1898992405, 7208159665, 27360619128, 103854959332, 394210908018, 1496339057640, 5679778471327, 21559206754217, 81834071700364

Offset

1,2

Comments

Column 3 of A297951.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-3) -2*a(n-4) -12*a(n-5) +24*a(n-6) +3*a(n-7) -4*a(n-8) -80*a(n-9) -67*a(n-10) +37*a(n-11) +140*a(n-12) +100*a(n-13) -32*a(n-14) -67*a(n-15) -12*a(n-16) +24*a(n-17) +2*a(n-18) -12*a(n-19) -4*a(n-20) for n>21

Example

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

Crossrefs

Cf. A297951.

Sequence in context: A041634 A044975 A251252 * A298384 A298765 A299460

Adjacent sequences: A297943 A297944 A297945 * A297947 A297948 A297949

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved