A300634 Number of nX3 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 6, 13, 34, 91, 253, 705, 1978, 5507, 15222, 41977, 115897, 320655, 888366, 2462325, 6824338, 18907933, 52373153, 145049587, 401721354, 1112657323, 3081952434, 8537004059, 23647611701, 65503496945, 181441284654, 502578971705

Offset

1,2

Comments

Column 3 of A300639.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -19*a(n-2) +28*a(n-3) -32*a(n-4) +42*a(n-5) -43*a(n-6) +23*a(n-7) -29*a(n-8) +16*a(n-9) +12*a(n-10) +64*a(n-11) +58*a(n-12) -110*a(n-13) -198*a(n-14) -136*a(n-15) +100*a(n-16) +236*a(n-17) +198*a(n-18) +90*a(n-19) +30*a(n-20) -16*a(n-21) -76*a(n-22) -64*a(n-23) +7*a(n-24) +23*a(n-25) -7*a(n-26) -20*a(n-27) -4*a(n-28) +10*a(n-29) +5*a(n-30) -a(n-31) -a(n-32)

Example

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

Crossrefs

Cf. A300639.

Sequence in context: A048693 A041068 A300430 * A301356 A037243 A107710

Adjacent sequences: A300631 A300632 A300633 * A300635 A300636 A300637

Keyword

nonn

Author

R. H. Hardin, Mar 10 2018

Status

approved