A205156 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..3 introduced in row major order

4, 159, 6941, 332285, 15821727, 754700909, 35987024999, 1716127952620, 81836397835786, 3902517029091331, 186098468293931598, 8874437930744029485, 423193413557085915551, 20180733461342796276880, 962354302788447192584715

Offset

1,1

Comments

Column 3 of A205161

Links

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

Formula

Empirical: a(n) = 31*a(n-1) +823*a(n-2) -252*a(n-3) -52259*a(n-4) +87947*a(n-5) +1095319*a(n-6) -4745176*a(n-7) +10623369*a(n-8) -36463721*a(n-9) +82619588*a(n-10) -158093875*a(n-11) +920330535*a(n-12) -1497234862*a(n-13) -5785171916*a(n-14) +16895441000*a(n-15) +6660128158*a(n-16) -55861945290*a(n-17) +14212421433*a(n-18) +108914824629*a(n-19) -51094288080*a(n-20) -179515412487*a(n-21) +82222065765*a(n-22) +259561632114*a(n-23) -111344938794*a(n-24) -259691826978*a(n-25) +151979086620*a(n-26) +155859261048*a(n-27) -153594572976*a(n-28) -39392244000*a(n-29) +97696264320*a(n-30) -14881397760*a(n-31) -40063040640*a(n-32) +13919817600*a(n-33) +10032346368*a(n-34) -4111699968*a(n-35) -1934917632*a(n-36) for n>39

Example

Some solutions for n=5
..0..1..0....0..0..1....0..1..0....0..0..1....0..1..1....0..0..1....0..1..0
..0..2..1....0..1..0....1..0..0....0..0..1....2..1..2....0..0..1....0..1..0
..1..0..0....2..2..1....0..1..1....2..3..2....3..0..1....1..2..2....1..2..1
..3..1..3....0..3..1....1..0..2....1..2..0....2..0..0....0..1..3....0..1..1
..0..1..0....0..1..0....3..0..1....1..0..0....1..3..0....1..3..3....3..3..0

Crossrefs

Sequence in context: A210837 A289231 A204680 * A268007 A205305 A268047

Adjacent sequences: A205153 A205154 A205155 * A205157 A205158 A205159

Keyword

nonn

Author

R. H. Hardin Jan 22 2012

Status

approved