A304006 Number of n X 4 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

1, 13, 21, 26, 64, 115, 211, 439, 870, 1725, 3513, 7141, 14372, 29438, 60518, 123439, 253860, 523477, 1075787, 2216143, 4575316, 9438222, 19480290, 40253428, 83178619, 171897255, 355448881, 735100437, 1520380599, 3145360038, 6508033432

Offset

1,2

Comments

Column 4 of A304010.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -6*a(n-2) -9*a(n-4) +8*a(n-5) +36*a(n-6) -29*a(n-7) +34*a(n-8) -88*a(n-9) +8*a(n-10) -70*a(n-11) +205*a(n-12) +66*a(n-13) -377*a(n-14) -29*a(n-15) +420*a(n-16) +897*a(n-17) -1329*a(n-18) -1792*a(n-19) +3267*a(n-20) +1953*a(n-21) -3000*a(n-22) -1986*a(n-23) -1836*a(n-24) +4857*a(n-25) -812*a(n-26) +2460*a(n-27) -5658*a(n-28) -21869*a(n-29) +5879*a(n-30) +37979*a(n-31) +39222*a(n-32) -53345*a(n-33) -60350*a(n-34) +80033*a(n-35) +55646*a(n-36) -80249*a(n-37) -99116*a(n-38) +97246*a(n-39) +113723*a(n-40) -115592*a(n-41) -82690*a(n-42) +63249*a(n-43) +23806*a(n-44) -67251*a(n-45) +52726*a(n-46) +64947*a(n-47) -59223*a(n-48) +4895*a(n-49) +22611*a(n-50) -5950*a(n-51) +1369*a(n-52) +5125*a(n-53) -13309*a(n-54) -19653*a(n-55) +5627*a(n-56) +2405*a(n-57) +1342*a(n-58) +2478*a(n-59) +2088*a(n-60) +435*a(n-61) -1017*a(n-62) -263*a(n-63) -116*a(n-64) +64*a(n-65) -96*a(n-66) +48*a(n-67) for n>70.

Example

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

Crossrefs

Cf. A304010.

Sequence in context: A032693 A049745 A332512 * A304948 A087683 A195375

Adjacent sequences: A304003 A304004 A304005 * A304007 A304008 A304009

Keyword

nonn

Author

R. H. Hardin, May 04 2018

Status

approved