%I #20 Jul 09 2015 20:28:59
%S 0,6,44,183
%N 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.
%C 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.
%C 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).
%C Writing a computer program to find further terms is desirable but beyond my expertise.
%e The case n = 2 is a special case since [curl (h curl v) = 0] is elliptic and so h = 0.
%K nonn,more
%O 2,2
%A _James Alexander Evans_, May 22 2015
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