A220714 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.

1, 26, 226, 2243, 21195, 201598, 1913495, 18172469, 172565016, 1638746380, 15562024443, 147782179281, 1403387239808, 13327022602525, 126557734357659, 1201833388741096, 11413000424299772, 108381561410710361

Offset

1,2

Comments

Column 3 of A220718.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) +31*a(n-2) -61*a(n-3) -118*a(n-4) +346*a(n-5) +321*a(n-6) -404*a(n-7) -191*a(n-8) -429*a(n-9) -270*a(n-10) +1567*a(n-11) -1015*a(n-12) -504*a(n-13) +179*a(n-14) -554*a(n-15) +136*a(n-16) +185*a(n-17) -21*a(n-18) -3*a(n-19) -a(n-20).

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...68.47.00...68.48.00...89.69.48...00.78.00...68.48.00...69.47.00
.38.68.24...23.79.78...29.26.47...26.14.12...39.29.78...26.24.78...38.17.00
.26.24.00...36.34.12...00.13.00...00.00.00...00.13.12...00.36.24...23.00.00

Crossrefs

Cf. A220718.

Sequence in context: A317865 A185553 A269658 * A159519 A110486 A098994

Adjacent sequences: A220711 A220712 A220713 * A220715 A220716 A220717

Keyword

nonn

Author

R. H. Hardin, Dec 18 2012

Status

approved