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

Author

N. J. A. Sloane, Sep 21 2009

Keywords

• nonn
• easy

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

Examples

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

Links

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

Crossrefs

Cf. A001333, A078469, A152124.

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