%I A143025
%S A143025 8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,
%T A143025 1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1,8,2,8,1
%N A143025 Numerator of 1/n^2-1/(3n)^2.
%C A143025 This can be generated from the transitions between principal quantum 
               numbers n and 3n in the Hydrogen series: A005563(2), A061037(6), 
               A061039(9), A061041(12), A061043(15), A061045(18), A061047(21), A061049(24),
               ... (The mention of A005563(2) is somewhat a fluke to maintain the 
               periodic pattern.)
%C A143025 Without first column (0's),square of A005563 and successive spectra is 
               shared in two triangles by principal separatrix period 3:repeat 3,
               3,1=A144437. 8,2,8,1 is the first of other (secondary) separatrices.
%F A143025 Period length 4: a(n+4)=a(n).
%Y A143025 Cf. A045944.
%Y A143025 Cf. A144437 for numerators of 1/n^2-1/(4n)^2.
%Y A143025 Sequence in context: A132716 A134724 A021551 this_sequence A085967 A143531 
               A019865
%Y A143025 Adjacent sequences: A143022 A143023 A143024 this_sequence A143026 A143027 
               A143028
%K A143025 nonn,uned
%O A143025 1,1
%A A143025 Paul Curtz (bpcrtz(AT)free.fr), Oct 13 2008
%E A143025 Partially edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 
               10 2008