A258156 Curl kernel sequence: a(n) is the number of independent constants on which an n-th-order tensor h can be shown to depend if the equation [curl (h nabla^{n-2}curl v)=0] is satisfied nontrivially for all vectors v.

0, 6, 44, 183

Offset

2,2

Comments

To calculate a(n) has been difficult. So far a brute force (by hand!) approach has been the only fruitful method. That is, writing the equation of consideration in index notation, taking a Fourier transform and solving a rather large system of linear equations in 3^n unknowns.

Based on observation, it is suspected that the sequence takes the form [0, n=2, 3^n - q(n), n>2], where q(n) is quadratic in n. The quadratic in question is hypothesized to be q(n)=(1/2)*(7*n^2-17*n+30).

Writing a computer program to find further terms is desirable but beyond my expertise.

Links

Table of n, a(n) for n=2..5.

Example

The case n = 2 is a special case since [curl (h curl v) = 0] is elliptic and so h = 0.

Crossrefs

Sequence in context: A075337 A000561 A292057 * A182540 A309418 A203601

Adjacent sequences: A258153 A258154 A258155 * A258157 A258158 A258159

Keyword

nonn,more

Author

James Alexander Evans, May 22 2015

Status

approved