A300423 Number of nX4 0..1 arrays with every element equal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

2, 30, 272, 2227, 18205, 150352, 1240541, 10232500, 84410206, 696309062, 5743948074, 47382634074, 390866061898, 3224309862212, 26597791554069, 219408975139223, 1809935922730538, 14930419523386359, 123163159741496460

Offset

1,1

Comments

Column 4 of A300427.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) +2*a(n-2) -67*a(n-3) -36*a(n-4) +250*a(n-5) +100*a(n-6) -337*a(n-7) -311*a(n-8) -4*a(n-9) +180*a(n-10) +1204*a(n-11) +368*a(n-12) -6713*a(n-13) +1814*a(n-14) +24164*a(n-15) -4030*a(n-16) -38947*a(n-17) +12663*a(n-18) +70432*a(n-19) -10144*a(n-20) -114955*a(n-21) -44953*a(n-22) +34295*a(n-23) -50431*a(n-24) -53119*a(n-25) +55368*a(n-26) +19801*a(n-27) -43336*a(n-28) -17045*a(n-29) -8457*a(n-30) -4910*a(n-31) +13442*a(n-32) +10577*a(n-33) +1491*a(n-34) +631*a(n-35) +1576*a(n-36) +8*a(n-37) -1962*a(n-38) -797*a(n-39) +165*a(n-40) +135*a(n-41) +129*a(n-42) +a(n-43) -24*a(n-44) -2*a(n-45) -a(n-46) +a(n-47) for n>49

Example

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

Crossrefs

Cf. A300427.

Sequence in context: A215237 A189103 A368498 * A300685 A300608 A301350

Adjacent sequences: A300420 A300421 A300422 * A300424 A300425 A300426

Keyword

nonn

Author

R. H. Hardin, Mar 05 2018

Status

approved