A318020 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

8, 35, 133, 569, 2227, 9063, 37030, 153117, 634563, 2638225, 10982346, 45752446, 190717173, 795215367, 3316427798, 13832535622, 57698440650, 240682257990, 1004002784204, 4188247714891, 17471641410509, 72884884003250

Offset

1,1

Comments

Column 4 of A318024.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -5*a(n-2) -43*a(n-3) +43*a(n-4) +80*a(n-5) -81*a(n-6) +389*a(n-7) -166*a(n-8) -1663*a(n-9) +73*a(n-10) +382*a(n-11) -1004*a(n-12) +8420*a(n-13) +7017*a(n-14) -4732*a(n-15) -2578*a(n-16) -13225*a(n-17) -39864*a(n-18) -12992*a(n-19) +17783*a(n-20) +22252*a(n-21) +68630*a(n-22) +66472*a(n-23) +38631*a(n-24) -11186*a(n-25) -59925*a(n-26) -74469*a(n-27) -118580*a(n-28) -92365*a(n-29) -52929*a(n-30) +71335*a(n-31) +62509*a(n-32) +51480*a(n-33) +109573*a(n-34) +66423*a(n-35) -5605*a(n-36) -21559*a(n-37) +22798*a(n-38) -67343*a(n-39) -60989*a(n-40) +24323*a(n-41) +1112*a(n-42) -37873*a(n-43) +24020*a(n-44) +38942*a(n-45) -22226*a(n-46) -5050*a(n-47) +18426*a(n-48) -1034*a(n-49) -17141*a(n-50) -3370*a(n-51) +11008*a(n-52) -3889*a(n-53) -7151*a(n-54) +4729*a(n-55) +4215*a(n-56) -2118*a(n-57) -1964*a(n-58) +3078*a(n-59) -463*a(n-60) -286*a(n-61) -1062*a(n-62) +1505*a(n-63) -828*a(n-64) -31*a(n-65) +196*a(n-66) -52*a(n-67) -33*a(n-68) +28*a(n-69) -4*a(n-70) for n>74

Example

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

Crossrefs

Cf. A318024.

Sequence in context: A292479 A301881 A094616 * A340522 A114569 A189599

Adjacent sequences: A318017 A318018 A318019 * A318021 A318022 A318023

Keyword

nonn

Author

R. H. Hardin, Aug 12 2018

Status

approved