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
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)
EXAMPLE
The pieces illustrating a(3) = 3 are:
AAA BB. .CC
AAA .BB CC.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 21 2009
STATUS
approved