This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A152113 #23 Jun 01 2024 12:01:14
%S A152113 1,1,3,3,7,7,17,17,41,41,99,99,239,239,577,577,1393,1393,3363,3363,
%T A152113 8119,8119,19601,19601,47321,47321,114243,114243,275807,275807,665857,
%U A152113 665857,1607521,1607521,3880899,3880899,9369319,9369319,22619537,22619537,54608393
%N A152113 A001333 with terms repeated.
%C A152113 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.
%C A152113 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
%H A152113 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,1).
%F A152113 From _Colin Barker_, Jul 14 2013: (Start)
%F A152113 a(n) = 2*a(n-2) + a(n-4).
%F A152113 G.f.: -x*(x+1)*(x^2+1) / (x^4+2*x^2-1). (End)
%F A152113 a(n+1) = A135153(n) + A135153(n+2). - _R. J. Mathar_, Jul 10 2019
%e A152113 The pieces illustrating a(3) = 3 are:
%e A152113 AAA BB. .CC
%e A152113 AAA .BB CC.
%Y A152113 Cf. A001333, A078469, A152124.
%K A152113 nonn,easy
%O A152113 1,3
%A A152113 _N. J. A. Sloane_, Sep 21 2009