A005290 Representation degeneracies for boson strings.

1, -1, 0, 0, 1, 0, 2, 0, 3, 1, 5, 2, 10, 5, 16, 13, 28, 24, 50, 46, 84, 87, 141, 153, 241, 266, 396, 459, 653, 766, 1070, 1267, 1725, 2075, 2762, 3342, 4397, 5330, 6918, 8432, 10814, 13188, 16784, 20468, 25836, 31529, 39505, 48169, 60033, 73092, 90597, 110203, 135920, 165058, 202754, 245774, 300707

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. L. Curtright and C. B. Thorn, Symmetry patterns in the mass spectra of dual string models, Nuclear Phys. B 274 (1986), 520-588. See Tables 6a and 6b.
• T. L. Curtright and Charles B. Thorn, Spin content of the bosonic string, Physics Letters B 175.1 (1986): 47-52.

Programs

Maple

M:=101:
p:=mul((1-x^n)^(-1),n=1..M):
G1:=J-> p^2*add( x^(n*J+n*(n-1)/2)*(-1)^(n-1)*(1-x^n)^2, n=1..M):
G2:=J->series(G1(J),x,M);
G3:=J->seriestolist(G2(J));
G3(0); # N. J. A. Sloane, Jul 11 2015

Formula

There is a g.f. due to J. Goldstone given in Eq. (5) of Curtright and Thorn (1986), and programmed in Maple below. - N. J. A. Sloane, Jul 11 2015