A210032 a(n)=n for n=1,2,3 and 4; a(n)=5 for n >= 5.

1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

A. Timothy Royappa, Mar 16 2012

Keywords

• easy
• nonn

Comments

In atomic spectroscopy, a(n) is the number of D term symbols with spin multiplicity equal to n, i.e., there is one singlet-D term (n=1), and there are two doublet-D terms (n=2), three triple-D terms (n=3), four quartet-D terms (n=4) and five terms for every other D term of multiplicity 5 or higher (n >= 5).

Decimal expansion of 11111/9000. - Arkadiusz Wesolowski, Mar 29 2012

Links

• Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A010716, A101272, A158411, A168092, A128999.

Programs

Mathematica

Join[Range@4, Table[5, {83}]] (* Arkadiusz Wesolowski, Mar 29 2012 *)
PadRight[{1,2,3,4},120,{5}] (* Harvey P. Dale, Sep 23 2017 *)

Formula

a(n) = min(n,5). - Wesley Ivan Hurt, Apr 16 2014

From Elmo R. Oliveira, Jun 26 2024: (Start)

G.f.: x*(1+x+x^2+x^3+x^4)/(1-x) = x*(1-x^5)/(1-x)^2.

a(n) = 1 + A158411(n-1) = A101272(n+1) - 1 = A168093(n-1) - 2. (End)