OFFSET
0,2
COMMENTS
Numerator of 1/n^2-1/(3n)^2 if n>0.
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.)
Related to the continued fraction of (12*sqrt(55)-72)/19 = 0.89444115.. = 0+1/(1+1/(8+1/(2+...))). - R. J. Mathar, Jun 27 2011
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).
FORMULA
a(n+4) = a(n).
G.f.: (1+8*x+2*x^2+8*x^3)/(1-x^4).
From Wesley Ivan Hurt, Jul 10 2016: (Start)
a(n) = (19 - 13*I^(2*n) - I^(-n) - I^n)/4, where I = sqrt(-1).
a(n) = (19 - 2*cos(n*Pi/2) - 13*cos(n*Pi))/4. (End)
MAPLE
seq(op([1, 8, 2, 8]), n=0..50); # Wesley Ivan Hurt, Jul 10 2016
MATHEMATICA
PadRight[{}, 120, {1, 8, 2, 8}] (* Harvey P. Dale, Jul 01 2015 *)
PROG
(PARI) a(n)=[1, 8, 2, 8][n%4+1] \\ Charles R Greathouse IV, Jun 02 2011
(Magma) &cat [[1, 8, 2, 8]^^30]; // Wesley Ivan Hurt, Jul 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 13 2008
EXTENSIONS
Partially edited by R. J. Mathar, Dec 10 2008
STATUS
approved