A303621 Number of nX5 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 72, 362, 3591, 37910, 398859, 4288358, 46208517, 499581127, 5409406326, 58631184705, 635886643605, 6899110045327, 74869703068990, 812605582421642, 8820444837792716, 95746681645850346, 1039371314814583752

Offset

1,2

Comments

Column 5 of A303624.

Links

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

Formula

Empirical: a(n) = 18*a(n-1) -88*a(n-2) +181*a(n-3) -901*a(n-4) +2154*a(n-5) -5035*a(n-6) +16596*a(n-7) -31806*a(n-8) +103835*a(n-9) -174793*a(n-10) +639689*a(n-11) -1015298*a(n-12) +2098982*a(n-13) -4679516*a(n-14) +681361*a(n-15) -12613662*a(n-16) -15526763*a(n-17) -10360518*a(n-18) -10900003*a(n-19) +93523754*a(n-20) +138980544*a(n-21) +294248039*a(n-22) +139392842*a(n-23) -25962616*a(n-24) -556388985*a(n-25) -738814401*a(n-26) -757930815*a(n-27) -359173350*a(n-28) +112140113*a(n-29) +449650391*a(n-30) +477280826*a(n-31) +290561830*a(n-32) +179957648*a(n-33) +43958819*a(n-34) +40164342*a(n-35) +66281759*a(n-36) +44868212*a(n-37) -71504876*a(n-38) -132574315*a(n-39) -159275867*a(n-40) -34904367*a(n-41) +75249340*a(n-42) +59334276*a(n-43) +13210549*a(n-44) -10299119*a(n-45) -21088861*a(n-46) -10663095*a(n-47) +6436916*a(n-48) +5938447*a(n-49) +1623325*a(n-50) -91939*a(n-51) +526515*a(n-52) +437625*a(n-53) +225322*a(n-54) +81564*a(n-55) +1567*a(n-56) +1935*a(n-57) +4592*a(n-58) -116*a(n-59) -232*a(n-60) +144*a(n-61) -64*a(n-62) for n>65

Example

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

Crossrefs

Cf. A303624.

Sequence in context: A090788 A334902 A192792 * A084479 A084478 A187158

Adjacent sequences: A303618 A303619 A303620 * A303622 A303623 A303624

Keyword

nonn

Author

R. H. Hardin, Apr 27 2018

Status

approved