A210032 - OEIS

%I #36 Nov 01 2024 12:40:55

%S 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,

%T 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,

%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

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

%C 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).

%C Decimal expansion of 11111/9000. - _Arkadiusz Wesolowski_, Mar 29 2012

%H Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F a(n) = min(n,5). - _Wesley Ivan Hurt_, Apr 16 2014

%F From _Elmo R. Oliveira_, Jun 26 2024: (Start)

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

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

%t Join[Range@4, Table[5, {83}]] (* _Arkadiusz Wesolowski_, Mar 29 2012 *)

%t PadRight[{1,2,3,4},120,{5}] (* _Harvey P. Dale_, Sep 23 2017 *)

%Y Cf. A010716, A101272, A158411, A168093.

%K easy,nonn

%O 1,2

%A _A. Timothy Royappa_, Mar 16 2012