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A171372
a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 1.
1
1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5
OFFSET
0,2
COMMENTS
The diagonal of a table of numerators of the Rydberg-Ritz spectrum of hydrogen:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... A000012
0, 5, 3, 21, 2, 45, 15, 77, 6, 117, 35, ... A061037
0, 9, 5, 33, 3, 65, 21, 105, 1, 153, 45, ... A061041
0, 13, 7, 5, 4, 85, 1, 133, 10, 7, 55, ... A061045
0, 17, 9, 57, 5, 105, 33, 161, 3, 225, 65, ... A061049
0, 21, 11, 69, 6, 1, 39, 189, 14, 261, 3, ...
0, 25, 13, 1, 7, 145, 5, 217, 1, 11, 85, ...
0, 29, 15, 93, 8, 165, 51, 5, 18, 333, 95, ...
0, 33, 17, 105, 9, 185, 57, 273, 5, 369, 105, ...
0, 37, 19, 13, 10, 205, 7, 301, 22, 5, 115, ...
0, 41, 21, 129, 11, 9, 69, 329, 3, 441, 1, ...
In that respect, constructed similar to A144437.
FORMULA
a(n) = numerator of 5/(6*n)^2 .
Period 5: repeat [1,5,5,5,5].
G.f.: (1 + 5*x + 5*x^2 + 5*x^3 + 5*x^4)/((1-x)*(1 + x + x^2 + x^3 + x^4)).
a(n) = 1 + 4*sign(n mod 5). - Wesley Ivan Hurt, Sep 26 2018
a(n) = (21-8*cos(2*n*Pi/5)-8*cos(4*n*Pi/5))/5. - Wesley Ivan Hurt, Sep 27 2018
MATHEMATICA
Table[If[n==0, 1, Numerator[5/(6*n)^2]], {n, 0, 100}] (* G. C. Greubel, Sep 20 2018 *)
PROG
(PARI) concat([1], vector(100, n, numerator(5/(6*n)^2))) \\ G. C. Greubel, Sep 20 2018
(Magma) [1] cat [Numerator(5/(6*n)^2): n in [1..100]]; // G. C. Greubel, Sep 20 2018
CROSSREFS
Cf. A171373 (binomial transform), A171408, A105371.
Sequence in context: A232614 A254609 A133707 * A083945 A125563 A093704
KEYWORD
nonn,easy,frac
AUTHOR
Paul Curtz, Dec 07 2009
EXTENSIONS
Edited by R. J. Mathar, Dec 15 2009
STATUS
approved