A300542 Number of n X 4 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

2, 37, 450, 5232, 61561, 724165, 8514930, 100122064, 1177281510, 13843038446, 162773058221, 1913963384213, 22505296146317, 264628027537059, 3111622815745035, 36587948139816223, 430218579935902604

Offset

1,1

Comments

Column 4 of A300546.

Links

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

Formula

Empirical: a(n) = 13*a(n-1) -10*a(n-2) -52*a(n-3) -39*a(n-4) +158*a(n-5) +182*a(n-6) -173*a(n-7) +204*a(n-8) -97*a(n-9) -2338*a(n-10) -899*a(n-11) +4496*a(n-12) +3707*a(n-13) +1000*a(n-14) +8464*a(n-15) -3055*a(n-16) -39432*a(n-17) -9440*a(n-18) +76130*a(n-19) +40914*a(n-20) -80801*a(n-21) -55238*a(n-22) +57105*a(n-23) +37666*a(n-24) -35103*a(n-25) -17842*a(n-26) +18065*a(n-27) +4848*a(n-28) -6808*a(n-29) +418*a(n-30) +1778*a(n-31) -1108*a(n-32) -131*a(n-33) +503*a(n-34) -83*a(n-35) -134*a(n-36) +52*a(n-37) +18*a(n-38) -11*a(n-39) -2*a(n-40) +a(n-41) for n > 42.

Example

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

Crossrefs

Cf. A300546.

Sequence in context: A001569 A092853 A297796 * A100849 A300969 A120047

Adjacent sequences: A300539 A300540 A300541 * A300543 A300544 A300545

Keyword

nonn

Author

R. H. Hardin, Mar 08 2018

Status

approved