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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, 1, 5, 37, 257, 1665, 10695, 68637, 440509, 2827377, 18148003, 116487861, 747713321, 4799439985, 30806785967, 197743565181, 1269282762917, 8147313444929, 52296241209451, 335680820572405, 2154679016567857 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)