A220648 Number of ways to reciprocally link elements of an nX3 array either to themselves or to exactly two king-move neighbors, without 3-loops

1, 23, 333, 4352, 59846, 816159, 11131560, 151872860, 2071881506, 28265332768, 385605987981, 5260573865475, 71766627731228, 979065962496791, 13356767420074715, 182217790214391903, 2485880154961341585

Offset

1,2

Comments

Column 3 of A220652

Links

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

Formula

Empirical: a(n) = 9*a(n-1) +55*a(n-2) +119*a(n-3) -44*a(n-4) -388*a(n-5) -58*a(n-6) +355*a(n-7) +79*a(n-8) -85*a(n-9) -13*a(n-10)

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
.00.67.48...00.69.47...00.89.00...68.46.47...00.00.00...00.67.48...89.67.47
.39.89.28...69.34.17...89.27.18...29.36.47...00.67.48...36.47.27...23.13.00
.00.12.12...00.13.00...23.16.24...00.13.00...36.46.24...36.34.00...00.00.00

Crossrefs

Sequence in context: A270498 A260727 A000543 * A243422 A028110 A163512

Adjacent sequences: A220645 A220646 A220647 * A220649 A220650 A220651

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved