A171372 a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 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.

Links

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

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

Adjacent sequences: A171369 A171370 A171371 * A171373 A171374 A171375

Keyword

nonn,easy,frac

Author

Paul Curtz, Dec 07 2009

Extensions

Edited by R. J. Mathar, Dec 15 2009

Status

approved