A152113 A001333 with terms repeated.

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

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.

a(n+2) is the number of palindromic words of length n on a 3-letter alphabet {a,b,c} which do not contain the "ab" subword. See A001906 for the words of length n on a 3-letter alphabet without "ab" subword but not necessarily palindromic. Example length 1: "a" or "b" or "c". Example length 2: "aa", "bb", "cc". Example length 3: There are 9 palindromic words but "aba" and "bab" are not admitted and only 7 remain. - R. J. Mathar, Jul 10 2019

Links

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

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

Formula

From Colin Barker, Jul 14 2013: (Start)

a(n) = 2*a(n-2) + a(n-4).

G.f.: -x*(x+1)*(x^2+1) / (x^4+2*x^2-1). (End)

a(n+1) = A135153(n) + A135153(n+2). - R. J. Mathar, Jul 10 2019

Example

The pieces illustrating a(3) = 3 are:
 AAA BB. .CC
 AAA .BB CC.

Crossrefs

Cf. A001333, A078469, A152124.

Sequence in context: A370202 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