

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(n2)+a(n4). G.f.: x*(x+1)*(x^2+1) / (x^4+2*x^21).  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



