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A220726 Number of ways to reciprocally link elements of a 2 X n array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors. 1
1, 2, 7, 21, 68, 221, 717, 2330, 7571, 24601, 79940, 259761, 844081, 2742802, 8912607, 28961101, 94107748, 305798741, 993678757, 3228912810, 10492201691, 34093920401, 110786605380, 359995910921, 1169789934761, 3801177874402 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 2 of A220725.

LINKS

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

FORMULA

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

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

EXAMPLE

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

.00.00.00...00.67.47...69.49.00...00.69.47...69.47.00...69.46.47...00.79.00

.00.00.00...36.34.00...00.16.14...00.36.14...36.14.00...00.13.00...36.46.14

CROSSREFS

Cf. A220725.

Sequence in context: A186240 A274203 A330058 * A347302 A127540 A339041

Adjacent sequences:  A220723 A220724 A220725 * A220727 A220728 A220729

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2012

STATUS

approved

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)