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A090666 Number of repetitions (defined as the number of appearances minus one) of L quantum number for a given value of N=2*nb+tau=0,1,2,... principal quantum number for the 5 dimensional harmonic oscillator (connected to the solution of Bohr equation in 5 dimensional). For each tau, nu=0,1,..,[tau/3] and K=tau-2*nu. Finally L=K,K+1,K+2,...,2*K-2,2*K (or alternatively from K to 2*K with the exception of 2*K-1). 0
0, 0, 0, 0, 2, 3, 7, 11, 18, 26, 36, 48, 63, 79, 99, 121, 146, 174, 206, 240, 279, 321, 367, 417, 472, 530, 594, 662, 735, 813, 897 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Nuclear Phyics, collective model: classification of states based on quantum numbers and group theory.

REFERENCES

L. Fortunato, Compendium on the solutions of the Bohr hamiltonian, in preparation (Dec. 2003).

LINKS

Table of n, a(n) for n=0..30.

L. Fortunato, Solutions of the Bohr hamiltonian, a compendium, arXiv:nucl-th/0411087, 2004; Eur. Phys. J. A26S1 (2005) 1-30. (arxiv preprint)

FORMULA

N = 2*nb+tau = 0, 1, 2, ..... nb=0, 1, 2, .... tau=0, 1, 2, .... nu=0, 1, .., [tau/3] K=tau-2*nu L=K, K+1, K+2, ..., 2*K-2, 2*K

G.f.: x^4*(x^2-x+1)*(x^5-x^4-2x^3+x+2)/((x-1)^4*(x+1)*(x^2+x+1)). - conjectured by Jean-Fran├žois Alcover, Feb 18 2019

EXAMPLE

a(N=0)=0 because N=0 implies nb=0 and tau=0. Hence nu=0, K=0 and L=0. There are no repetitions.

a(N=4)=2 because N=2 implies (nb,tau)= (0,4),(1,2),(2,0). At the end L=0,2,4,2,4,4,5,6,8, so that only 2 repetitions are found.

PROG

(FORTRAN 77) implicit integer(a-z) dimension mrep(0:100) do N=0, 30 do L=0, 100 mrep(L)=0 enddo do nb=0, nint(real(N)/2.-0.01) tau=N-2*nb numax=int(tau/3) do nu=0, numax K=tau-3*nu do L=K, 2*K if(L.eq.(2*K-1)) goto 100 mrep(L)=mrep(L)+1 100 enddo enddo enddo sum=0 do L=0, 100 if(mrep(L).gt.0) then sum=sum+mrep(L)-1 endif enddo print *, N, sum enddo end

CROSSREFS

Sequence in context: A060341 A114345 A077165 * A140409 A201011 A108541

Adjacent sequences:  A090663 A090664 A090665 * A090667 A090668 A090669

KEYWORD

nonn,more

AUTHOR

Lorenzo Fortunato (fortunat(AT)pd.infn.it), Dec 16 2003

STATUS

approved

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Last modified February 24 20:33 EST 2020. Contains 332210 sequences. (Running on oeis4.)