A298129 Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

0, 5, 13, 15, 233, 1055, 5782, 36225, 205348, 1209336, 7104221, 41593299, 244217670, 1432727023, 8406086075, 49326923443, 289428447489, 1698283766510, 9965061067996, 58472010523076, 343097200672431, 2013196295930588

Offset

1,2

Comments

Column 4 of A298133.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +18*a(n-2) +25*a(n-3) -115*a(n-4) -418*a(n-5) -362*a(n-6) +1223*a(n-7) +4240*a(n-8) +2290*a(n-9) -9359*a(n-10) -16112*a(n-11) +3825*a(n-12) +30881*a(n-13) +10497*a(n-14) -37030*a(n-15) -21624*a(n-16) +40949*a(n-17) +30128*a(n-18) -52580*a(n-19) -29839*a(n-20) +16613*a(n-21) -97187*a(n-22) -8185*a(n-23) +199948*a(n-24) +235970*a(n-25) +21467*a(n-26) -396028*a(n-27) -168777*a(n-28) +347284*a(n-29) +546093*a(n-30) -20595*a(n-31) -733067*a(n-32) -497232*a(n-33) +64780*a(n-34) +471056*a(n-35) +244089*a(n-36) -113651*a(n-37) -210162*a(n-38) -106774*a(n-39) +42085*a(n-40) -11265*a(n-41) -9272*a(n-42) +5459*a(n-43) +12341*a(n-44) +24615*a(n-45) +7030*a(n-46) -4538*a(n-47) -4658*a(n-48) -2118*a(n-49) +128*a(n-50) +580*a(n-51) -4*a(n-52) -40*a(n-53) for n>56

Example

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

Crossrefs

Cf. A298133.

Sequence in context: A067696 A050598 A297862 * A158334 A282747 A088908

Adjacent sequences: A298126 A298127 A298128 * A298130 A298131 A298132

Keyword

nonn

Author

R. H. Hardin, Jan 13 2018

Status

approved