A298723 Number of nX4 0..1 arrays with every element equal to 0, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 18, 15, 34, 77, 230, 712, 2167, 6694, 20775, 64197, 200062, 624696, 1949420, 6084096, 19000957, 59343184, 185364275, 579116320, 1809395723, 5653433396, 17664869660, 55197920461, 172481319644, 538973897693, 1684218210917

Offset

1,2

Comments

Column 4 of A298727.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -9*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +15*a(n-6) +26*a(n-7) -157*a(n-8) +466*a(n-9) -220*a(n-10) -444*a(n-11) +96*a(n-12) -157*a(n-13) -652*a(n-14) +146*a(n-15) +1984*a(n-16) +130*a(n-17) +2025*a(n-18) -2473*a(n-19) +6365*a(n-20) -4168*a(n-21) -11764*a(n-22) +5390*a(n-23) -9469*a(n-24) +8003*a(n-25) -14173*a(n-26) +26192*a(n-27) -10436*a(n-28) +27101*a(n-29) -15251*a(n-30) +9559*a(n-31) +14483*a(n-32) -50379*a(n-33) +34809*a(n-34) -58786*a(n-35) +60997*a(n-36) -73488*a(n-37) +83309*a(n-38) -55321*a(n-39) +43987*a(n-40) -38228*a(n-41) +37989*a(n-42) -14291*a(n-43) +2903*a(n-44) -12735*a(n-45) +11717*a(n-46) -10534*a(n-47) +5177*a(n-48) +1621*a(n-49) +1470*a(n-50) -2283*a(n-51) -323*a(n-52) -752*a(n-53) +511*a(n-54) +22*a(n-55) +60*a(n-56) -80*a(n-57) +16*a(n-58) for n>60

Example

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

Crossrefs

Cf. A298727.

Sequence in context: A160901 A159502 A077668 * A299557 A079293 A070646

Adjacent sequences: A298720 A298721 A298722 * A298724 A298725 A298726

Keyword

nonn

Author

R. H. Hardin, Jan 25 2018

Status

approved