A220598 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops

1, 17, 471, 9047, 167614, 3174778, 60138423, 1137615308, 21523535122, 407249783145, 7705461280893, 145792738613760, 2758505816300670, 52192947928719778, 987528662199324496, 18684763495713245969

Offset

1,2

Comments

Column 4 of A220602

Links

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

Formula

Empirical: a(n) = 15*a(n-1) +41*a(n-2) +606*a(n-3) +405*a(n-4) +679*a(n-5) -8407*a(n-6) -28555*a(n-7) +17039*a(n-8) +147483*a(n-9) +79534*a(n-10) -260454*a(n-11) -334003*a(n-12) +79493*a(n-13) +384190*a(n-14) +187418*a(n-15) -93878*a(n-16) -122508*a(n-17) -48185*a(n-18) -5142*a(n-19) +3204*a(n-20) +1023*a(n-21) +22*a(n-22) -9*a(n-23) -11*a(n-24) +a(n-25)

Example

Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.68.46.48...68.48.67.47...00.67.46.48...68.48.00.78...00.68.48.78
.00.27.00.28...28.23.36.48...38.67.47.28...26.24.37.28...00.27.23.28
.36.46.46.24...26.46.46.24...23.36.46.24...00.36.46.24...36.46.46.24

Crossrefs

Sequence in context: A035276 A196484 A196717 * A239926 A111920 A296740

Adjacent sequences: A220595 A220596 A220597 * A220599 A220600 A220601

Keyword

nonn

Author

R. H. Hardin Dec 16 2012

Status

approved