A111100 Coefficient (times -1) of the 1/r^(2n) term in the radial far-field expansion of the squared amplitude of a doubly-charged topological point defect (-2 or +2 vortex) in the two-dimensional Ginzburg-Landau equation.

4, 8, 112, 2720, 103552, 5764352, 445521664, 45890802176, 6094567045120, 1015769696055296, 207796011483160576, 51221187819965530112, 14979210670593626472448, 5128843038563324804464640, 2032875137444937697755332608, 923598907664745712876929548288

Offset

1,1

Comments

Ginzburg-Landau vortex solutions are fundamental in the study of superconductors and superfluids.

Links

Table of n, a(n) for n=1..16.

Example

a(3) = 112 because A(r)^2 = 1- 4/r^2 - 8/r^4 - 112/r^6 - ...

Mathematica

n = 17;
v = 2;
sol = AsymptoticDSolveValue[{4 z^3 f''[z] + 4 z^2 f'[z] - f[z] v^2 z + (1 - f[z]^2) f[z] == 0, f[0] == 1}, f[z], {z, 0, n}];
Rest@CoefficientList[1 - sol^2 + O[z]^n, z] (* Andrey Zabolotskiy, Aug 04 2023 *)

Crossrefs

Cf. A110818.

Sequence in context: A336795 A273060 A215844 * A105036 A012940 A182967

Adjacent sequences: A111097 A111098 A111099 * A111101 A111102 A111103

Keyword

nonn

Author

Greg Huber, Oct 13 2005

Extensions

Terms a(11) and beyond from Andrey Zabolotskiy, Aug 04 2023

Status

approved