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A220709 Number of ways to reciprocally link elements of a 4 X n array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links. 1
1, 1, 5, 13, 37, 105, 298, 846, 2404, 6826, 19394, 55081, 156473, 444445, 1262497, 3586113, 10186570, 28935186, 82191652, 233468038, 663174914, 1883771569, 5350922525, 15199487245, 43174696525, 122639283705, 348361331050 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 4 of A220708.

LINKS

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

FORMULA

Empirical: a(n) = a(n-1) + 6*a(n-2) - 6*a(n-4) - a(n-5) + a(n-6) for n>7.

Empirical g.f.: x*(1 - 2*x^2 + 2*x^3 - 3*x^5 + x^6) / ((1 - x)*(1 + x)*(1 - x - 5*x^2 - x^3 + x^4)). - 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

.00.67.47...00.00.00...36.34.00...36.34.00...00.00.00

.36.34.00...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

CROSSREFS

Cf. A220708.

Sequence in context: A269803 A298417 A193642 * A182312 A071100 A199108

Adjacent sequences:  A220706 A220707 A220708 * A220710 A220711 A220712

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2012

STATUS

approved

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Last modified May 30 15:43 EDT 2020. Contains 334726 sequences. (Running on oeis4.)