A220634 Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

1, 1, 5, 37, 257, 1665, 10695, 68637, 440509, 2827377, 18148003, 116487861, 747713321, 4799439985, 30806785967, 197743565181, 1269282762917, 8147313444929, 52296241209451, 335680820572405, 2154679016567857

Offset

1,3

Comments

Row 4 of A220632.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 16*a(n-2) - 6*a(n-3) + 15*a(n-4) + a(n-5) - 2*a(n-6) for n>9.

Empirical g.f.: x*(1 - 8*x + 12*x^2 + 14*x^3 - 5*x^4 - 42*x^5 - 30*x^6 + 6*x^7 + 4*x^8) / ((1 - x)*(1 - 2*x - x^2)*(1 - 6*x - 3*x^2 + 2*x^3)). - Colin Barker, Aug 02 2018

Example

All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
.00.00.00...00.00.00...00.67.47...00.67.47...00.00.00
.00.00.00...00.00.00...36.34.00...36.34.00...00.67.47
.00.67.47...00.00.00...00.67.47...00.00.00...36.34.00
.36.34.00...00.00.00...36.34.00...00.00.00...00.00.00

Crossrefs

Cf. A220632.

Sequence in context: A108049 A121141 A331449 * A083232 A236581 A262410

Adjacent sequences: A220631 A220632 A220633 * A220635 A220636 A220637

Keyword

nonn

Author

R. H. Hardin, Dec 17 2012

Status

approved