A318013 Number of nX5 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

16, 338, 2130, 17703, 133136, 1033121, 7960400, 61442813, 473867122, 3655208840, 28191776637, 217440594949, 1677091399950, 12935220273973, 99767850363242, 769498052672954, 5935050680553926, 45776370159339585, 353067930786737702

Offset

1,1

Comments

Column 5 of A318016.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) +20*a(n-2) -178*a(n-3) -133*a(n-4) +1457*a(n-5) +229*a(n-6) -3767*a(n-7) +1604*a(n-8) -17083*a(n-9) -20904*a(n-10) +173201*a(n-11) +202212*a(n-12) -831126*a(n-13) -1256182*a(n-14) +3403061*a(n-15) +4253774*a(n-16) -11699625*a(n-17) -6680097*a(n-18) +28322072*a(n-19) -2645665*a(n-20) -40790067*a(n-21) +36479997*a(n-22) +11280476*a(n-23) -84094546*a(n-24) +101624162*a(n-25) +93470289*a(n-26) -282983523*a(n-27) -12820853*a(n-28) +436883259*a(n-29) -136772424*a(n-30) -458227773*a(n-31) +261645068*a(n-32) +329222395*a(n-33) -281524971*a(n-34) -137294396*a(n-35) +208179168*a(n-36) -13787843*a(n-37) -110888096*a(n-38) +82675746*a(n-39) +35123902*a(n-40) -80847975*a(n-41) +4683984*a(n-42) +47836163*a(n-43) -13649560*a(n-44) -19626484*a(n-45) +9320839*a(n-46) +5634785*a(n-47) -3908759*a(n-48) -924491*a(n-49) +943722*a(n-50) +32289*a(n-51) -77166*a(n-52) +7151*a(n-53) -17074*a(n-54) -886*a(n-55) +5570*a(n-56) +391*a(n-57) -465*a(n-58) -5*a(n-59) +6*a(n-60) -2*a(n-61) for n>65

Example

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

Crossrefs

Cf. A318016.

Sequence in context: A068368 A013993 A058722 * A320399 A173906 A227102

Adjacent sequences: A318010 A318011 A318012 * A318014 A318015 A318016

Keyword

nonn

Author

R. H. Hardin, Aug 12 2018

Status

approved