A302363 Number of nX4 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 20, 20, 77, 209, 774, 3143, 13556, 60280, 272792, 1243804, 5692133, 26100174, 119782344, 549950950, 2525484907, 11598683442, 53271277746, 244673796303, 1123793697954, 5161643580014, 23707760958131, 108891405413647

Offset

1,2

Comments

Column 4 of A302367.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -7*a(n-2) +10*a(n-3) -30*a(n-4) -21*a(n-5) -3*a(n-6) -68*a(n-7) +280*a(n-8) +414*a(n-9) +164*a(n-10) -423*a(n-11) -1527*a(n-12) +833*a(n-13) +1714*a(n-14) -2022*a(n-15) -1901*a(n-16) +367*a(n-17) +2024*a(n-18) +923*a(n-19) +66*a(n-20) -142*a(n-21) -5380*a(n-22) +4543*a(n-23) +13152*a(n-24) -11763*a(n-25) -12833*a(n-26) +16700*a(n-27) +4765*a(n-28) -15572*a(n-29) +1243*a(n-30) +9288*a(n-31) -3398*a(n-32) -4331*a(n-33) +2341*a(n-34) +1523*a(n-35) -1099*a(n-36) -619*a(n-37) +631*a(n-38) +476*a(n-39) -262*a(n-40) -191*a(n-41) +217*a(n-42) -15*a(n-43) -90*a(n-44) +18*a(n-45) +6*a(n-46) -14*a(n-47) +4*a(n-48) +6*a(n-49) -2*a(n-50) for n>53

Example

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

Crossrefs

Cf. A302367.

Sequence in context: A040381 A354569 A022354 * A165841 A222958 A374170

Adjacent sequences: A302360 A302361 A302362 * A302364 A302365 A302366

Keyword

nonn

Author

R. H. Hardin, Apr 06 2018

Status

approved