A298926 Number of n X 4 0..1 arrays with every element equal to 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 2, 4, 11, 23, 72, 201, 597, 1717, 5183, 15479, 46260, 138928, 417427, 1255369, 3777004, 11372190, 34247960, 103164581, 310821235, 936579808, 2822417917, 8506019597, 25636254701, 77267796877, 232891865309, 701970354408

Offset

1,2

Comments

Column 4 of A298930.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -10*a(n-2) +7*a(n-3) -23*a(n-4) +31*a(n-5) -15*a(n-6) +104*a(n-7) -147*a(n-8) +182*a(n-9) -366*a(n-10) +376*a(n-11) -685*a(n-12) +689*a(n-13) -613*a(n-14) +1143*a(n-15) -710*a(n-16) -129*a(n-17) -82*a(n-18) -584*a(n-19) +5620*a(n-20) -1356*a(n-21) +6298*a(n-22) -15575*a(n-23) +6568*a(n-24) -15985*a(n-25) +6661*a(n-26) -23488*a(n-27) +19556*a(n-28) +16109*a(n-29) +18333*a(n-30) +8059*a(n-31) -12197*a(n-32) +16533*a(n-33) -27875*a(n-34) -8576*a(n-35) -28209*a(n-36) +16299*a(n-37) +26487*a(n-38) +4040*a(n-39) -22226*a(n-40) +1134*a(n-41) -9128*a(n-42) -7294*a(n-43) +16692*a(n-44) +6504*a(n-45) +1137*a(n-46) -5253*a(n-47) +2127*a(n-48) -324*a(n-49) +1885*a(n-50) -1689*a(n-51) -59*a(n-52) -235*a(n-53) +346*a(n-54) -86*a(n-55) +12*a(n-56) -46*a(n-57) +24*a(n-58) +8*a(n-59) -4*a(n-60) for n>61.

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..0
..0..1..0..1. .0..1..1..0. .0..0..0..0. .0..1..0..1. .0..1..1..0
..1..1..0..1. .1..0..1..0. .0..0..0..0. .0..1..0..1. .0..1..0..1
..0..1..0..1. .1..0..1..0. .1..1..1..1. .1..0..0..1. .1..0..0..1
..0..0..1..1. .1..1..0..0. .1..1..1..1. .1..1..1..1. .1..1..1..1

Crossrefs

Cf. A298930.

Sequence in context: A006452 A104430 A298255 * A292157 A256801 A103669

Adjacent sequences: A298923 A298924 A298925 * A298927 A298928 A298929

Keyword

nonn

Author

R. H. Hardin, Jan 29 2018

Status

approved