A297974 Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 6, 20, 109, 1042, 7302, 60427, 481401, 3880101, 31362126, 253173482, 2046556093, 16538800168, 133678574420, 1080493649567, 8733450448870, 70591761501494, 570587091826725, 4612015763383176, 37278608281287313, 301320519515942968

Offset

1,2

Comments

Column 4 of A297978.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) +32*a(n-2) -140*a(n-3) -598*a(n-4) +1159*a(n-5) +5304*a(n-6) -4333*a(n-7) -25781*a(n-8) +7663*a(n-9) +77338*a(n-10) -9186*a(n-11) -146950*a(n-12) +40670*a(n-13) +162366*a(n-14) -251269*a(n-15) -5153*a(n-16) +716034*a(n-17) -170543*a(n-18) -1303137*a(n-19) +206096*a(n-20) +1281221*a(n-21) +682644*a(n-22) -1324101*a(n-23) -1132741*a(n-24) +1131408*a(n-25) +172656*a(n-26) +40049*a(n-27) -568390*a(n-28) -239758*a(n-29) +645066*a(n-30) -100658*a(n-31) -51639*a(n-32) +38776*a(n-33) +33836*a(n-34) +41437*a(n-35) -48047*a(n-36) -59151*a(n-37) +9515*a(n-38) +46874*a(n-39) -834*a(n-40) -25695*a(n-41) +1922*a(n-42) +7078*a(n-43) -1180*a(n-44) -1468*a(n-45) +204*a(n-46) for n>49

Example

Some solutions for n=7
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..1
..0..1..0..0. .1..1..0..0. .0..0..1..0. .1..1..1..1. .0..1..0..0
..0..1..1..0. .1..0..0..1. .0..1..1..0. .1..0..1..0. .1..1..1..0
..0..1..1..0. .0..0..1..1. .0..1..1..0. .0..1..0..0. .0..1..1..1
..0..1..1..0. .1..0..1..0. .0..0..1..0. .0..1..1..0. .0..0..0..1
..0..0..0..0. .1..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1

Crossrefs

Cf. A297978.

Sequence in context: A211953 A266846 A207819 * A280187 A151493 A036755

Adjacent sequences: A297971 A297972 A297973 * A297975 A297976 A297977

Keyword

nonn

Author

R. H. Hardin, Jan 10 2018

Status

approved