A300461 Number of nX4 0..1 arrays with every element equal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 4, 8, 28, 142, 540, 2585, 11343, 51501, 233028, 1052448, 4769842, 21579345, 97715668, 442378911, 2002838338, 9067930634, 41054700887, 185876096558, 841553822832, 3810142997823, 17250454214015, 78101569076062

Offset

1,2

Comments

Column 4 of A300465.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +6*a(n-2) -5*a(n-3) -37*a(n-4) -59*a(n-5) -39*a(n-6) +80*a(n-7) -279*a(n-8) +328*a(n-9) +1083*a(n-10) -25*a(n-11) +6234*a(n-12) +6280*a(n-13) -5927*a(n-14) +13954*a(n-15) -677*a(n-16) -53183*a(n-17) +32616*a(n-18) -49693*a(n-19) -57573*a(n-20) +142653*a(n-21) -126299*a(n-22) +100762*a(n-23) +71676*a(n-24) -234851*a(n-25) +178322*a(n-26) -92379*a(n-27) -11243*a(n-28) +181969*a(n-29) -91225*a(n-30) +44201*a(n-31) -9047*a(n-32) -83657*a(n-33) +21643*a(n-34) +39079*a(n-35) -7039*a(n-36) -11806*a(n-37) +2726*a(n-38) +9392*a(n-39) -18923*a(n-40) +27265*a(n-41) -28247*a(n-42) +17148*a(n-43) -7200*a(n-44) +2338*a(n-45) +517*a(n-46) -867*a(n-47) -170*a(n-48) +576*a(n-49) -297*a(n-50) +60*a(n-51) -4*a(n-52) for n>54

Example

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

Crossrefs

Cf. A300465.

Sequence in context: A143555 A025234 A075308 * A280085 A322784 A297638

Adjacent sequences: A300458 A300459 A300460 * A300462 A300463 A300464

Keyword

nonn

Author

R. H. Hardin, Mar 06 2018

Status

approved