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A220720 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors. 1
1, 7, 30, 126, 534, 2275, 9667, 41089, 174660, 742428, 3155820, 13414405, 57020437, 242375995, 1030264362, 4379330826, 18615162402, 79127219431, 336345003127, 1429697162869, 6077194423824, 25832248272072, 109804788896376 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A220725.

LINKS

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

FORMULA

Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + 5*a(n-3) + 3*a(n-4) - 2*a(n-5).

Empirical g.f.: x*(1 + 4*x + 5*x^2 + 3*x^3 - 2*x^4) / ((1 + x)*(1 - 4*x - 5*x^3 + 2*x^4)). - Colin Barker, Aug 02 2018

EXAMPLE

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):

.69.49.00...69.47.00...00.00.00...00.79.00...69.47.00...00.69.47...00.79.00

.00.17.17...39.16.47...00.69.47...39.69.14...39.19.00...00.36.14...36.49.17

.36.34.00...00.13.00...00.36.14...00.16.14...00.16.14...00.00.00...00.36.14

CROSSREFS

Cf. A220725.

Sequence in context: A037709 A037611 A171472 * A024311 A210100 A297080

Adjacent sequences:  A220717 A220718 A220719 * A220721 A220722 A220723

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2012

STATUS

approved

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Last modified January 17 09:32 EST 2020. Contains 330949 sequences. (Running on oeis4.)