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A171372
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a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 1.
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1
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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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) = 4*(n^4 mod 5)+1, with n >= 0. - Paolo P. Lava, Dec 14 2009
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
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MATHEMATICA
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Table[If[n==0, 1, Numerator[5/(6*n)^2]], {n, 0, 100}] (* G. C. Greubel, Sep 20 2018 *)
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PROG
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(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
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CROSSREFS
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Cf. A171373 (binomial transform), A171408, A105371.
Sequence in context: A232614 A254609 A133707 * A083945 A125563 A093704
Adjacent sequences: A171369 A171370 A171371 * A171373 A171374 A171375
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Paul Curtz, Dec 07 2009
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EXTENSIONS
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Edited by R. J. Mathar, Dec 15 2009
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STATUS
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approved
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