A317811 Number of nX4 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 3, 4, 7, 34, 56, 77, 228, 551, 1300, 3171, 6929, 16038, 38283, 89884, 210213, 489040, 1140562, 2668604, 6250857, 14610077, 34124180, 79756933, 186440331, 435962650, 1019155893, 2382147016, 5568392343, 13017040048, 30430709271, 71136801083

Offset

1,2

Comments

Column 4 of A317815.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) +8*a(n-5) -27*a(n-6) -20*a(n-7) -25*a(n-8) +70*a(n-9) +24*a(n-10) +124*a(n-11) +86*a(n-12) -80*a(n-13) -377*a(n-14) -343*a(n-15) -193*a(n-16) +448*a(n-17) +876*a(n-18) +779*a(n-19) -318*a(n-20) -936*a(n-21) -1187*a(n-22) -832*a(n-23) +863*a(n-24) +974*a(n-25) +1386*a(n-26) +118*a(n-27) -382*a(n-28) -1152*a(n-29) -661*a(n-30) +95*a(n-31) +336*a(n-32) +620*a(n-33) -201*a(n-34) +174*a(n-35) -269*a(n-36) +136*a(n-37) -152*a(n-38) +49*a(n-39) -76*a(n-40) +46*a(n-41) +11*a(n-42) -4*a(n-43) +16*a(n-44) -5*a(n-45) -a(n-48) for n>52

Example

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

Crossrefs

Cf. A317815.

Sequence in context: A007677 A042773 A042173 * A046461 A375268 A084590

Adjacent sequences: A317808 A317809 A317810 * A317812 A317813 A317814

Keyword

nonn

Author

R. H. Hardin, Aug 07 2018

Status

approved