A061047 Numerator of 1/49 - 1/n^2.

0, 15, 32, 51, 72, 95, 120, 3, 176, 207, 240, 275, 312, 351, 8, 435, 480, 527, 576, 627, 680, 15, 792, 851, 912, 975, 1040, 1107, 24, 1247, 1320, 1395, 1472, 1551, 1632, 5, 1800, 1887, 1976, 2067, 2160, 2255, 48, 2451, 2552, 2655, 2760, 2867

Offset: 7

Author

N. J. A. Sloane, May 26 2001

Keywords

• nonn
• frac

Comments

a(n) = (n+7)^2-49 = n*(n+14) = A098848(n), except a(7p). The corresponding series of atomic transitions is named Hansen-Strong. It comes after Lyman (1906-1914), Balmer (1885), Paschen (1908), Brackett (1922), Pfund (1924) and Humphreys series (1952 not 1953, justified later). - Paul Curtz, Oct 07 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 7..1000
• Peter Hansen and John Strong, Seventh Series of Atomic Hydrogen, Applied Optics, vol 12, 2, (Feb 1973), pp. 429-430. [From _Paul Curtz_, Oct 07 2008]

Crossrefs

Cf. A061035-A061050.

Cf. A061039, A061043, A045944, A098848.

Programs

Magma

[Numerator(1/49-1/n^2): n in [7..60]]; // Vincenzo Librandi, Sep 07 2016

Mathematica

Table[Numerator[1/49-1/n^2],{n,7,70}] (* Harvey P. Dale, Apr 26 2016 *)

PARI

a(n) = numerator(1/49 - 1/n^2); \\ Michel Marcus, Aug 15 2013

Extensions

Edited by M. F. Hasler, Nov 17 2014