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A152113 A001333 with terms repeated. 3
1, 1, 3, 3, 7, 7, 17, 17, 41, 41, 99, 99, 239, 239, 577, 577, 1393, 1393, 3363, 3363, 8119, 8119, 19601, 19601, 47321, 47321, 114243, 114243, 275807, 275807, 665857, 665857, 1607521, 1607521, 3880899, 3880899, 9369319, 9369319, 22619537, 22619537, 54608393 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Suggested by an email message from Hugo van der Sanden, Mar 23 2009, who says: Consider the partitions of a 2 x n rectangle into connected pieces consisting of unit squares cut along lattice lines. Then a(n) is the number of distinct pieces with rotational symmetry that extend to opposite corners.

LINKS

Table of n, a(n) for n=1..41.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,1).

FORMULA

a(n) = 2*a(n-2)+a(n-4). G.f.: -x*(x+1)*(x^2+1) / (x^4+2*x^2-1). - Colin Barker, Jul 14 2013

EXAMPLE

Example: the pieces illustrating a(3) = 3 are:

AAA BB. .CC

AAA .BB CC.

CROSSREFS

Cf. A001333, A078469, A152124.

Sequence in context: A174583 A226781 A147144 * A146149 A263795 A070925

Adjacent sequences:  A152110 A152111 A152112 * A152114 A152115 A152116

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 21 2009

STATUS

approved

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Last modified February 23 23:56 EST 2018. Contains 299595 sequences. (Running on oeis4.)