A298497 Number of nX4 0..1 arrays with every element equal to 0, 1, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

5, 13, 4, 38, 54, 97, 467, 1105, 3354, 12283, 37107, 122676, 416829, 1349661, 4501298, 15041030, 49602808, 165300728, 550279765, 1824434359, 6073061606, 20198360859, 67084559733, 223165737677, 742040901129, 2466100981652, 8201311431601

Offset

1,1

Comments

Column 4 of A298501.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +38*a(n-3) -74*a(n-4) -94*a(n-5) -548*a(n-6) +1068*a(n-7) +1218*a(n-8) +4225*a(n-9) -8296*a(n-10) -8891*a(n-11) -20219*a(n-12) +40048*a(n-13) +41055*a(n-14) +65345*a(n-15) -129516*a(n-16) -127567*a(n-17) -150411*a(n-18) +291882*a(n-19) +277454*a(n-20) +255085*a(n-21) -466458*a(n-22) -433314*a(n-23) -325005*a(n-24) +528945*a(n-25) +492165*a(n-26) +313348*a(n-27) -417649*a(n-28) -405446*a(n-29) -226960*a(n-30) +216825*a(n-31) +235781*a(n-32) +118928*a(n-33) -61334*a(n-34) -89164*a(n-35) -39557*a(n-36) +263*a(n-37) +16190*a(n-38) +3967*a(n-39) +5305*a(n-40) +1954*a(n-41) +2833*a(n-42) -770*a(n-43) -1558*a(n-44) -1215*a(n-45) -319*a(n-46) +210*a(n-47) +145*a(n-48) +78*a(n-49) +4*a(n-50) +2*a(n-51) for n>54

Example

Some solutions for n=6
..0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..0..1. .0..1..0..1
..1..0..1..1. .1..1..0..0. .1..1..0..1. .1..1..0..0. .1..0..0..0
..0..0..1..0. .1..1..0..1. .0..1..0..0. .1..1..0..1. .1..1..0..1
..1..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..0..1. .1..1..0..1
..0..0..1..1. .0..0..1..1. .0..1..0..0. .1..1..0..0. .1..0..0..0
..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..1..0..0. .0..1..0..1

Crossrefs

Cf. A298501.

Sequence in context: A121645 A057691 A297903 * A246922 A246921 A170864

Adjacent sequences: A298494 A298495 A298496 * A298498 A298499 A298500

Keyword

nonn

Author

R. H. Hardin, Jan 20 2018

Status

approved