Thanks to everyone, I now have this working. Here is the final version.

--8<---------------cut here---------------start------------->8---
#+LATEX_HEADER: \usepackage{tikz}

First execute the second code block, to define the convenience macro
and to set the required new variables in ob-latex.el.  Then export to
HTML and to pdf to see the tree exported as an SVG image and as
embedded tikz respectively.

* Tikz test
Here's a tree, exported to both html and pdf.

#+header: :file (by-backend (html "tree.svg") (latex "tree.tikz") (t "tree.png"))
#+header: :imagemagick yes :iminoptions -density 600 :imoutoptions -geometry 800
#+header: :results file raw
#+header: :fit yes
#+header: :headers '("\\usepackage{tikz}")
#+begin_src latex
  \usetikzlibrary{trees}
  \begin{tikzpicture}
    \node [circle, draw, fill=red!20] at (0,0) {1}
    child { node [circle, draw, fill=blue!30] {2}
      child { node [circle, draw, fill=green!30] {3} }
      child { node [circle, draw, fill=yellow!30] {4} }};
  \end{tikzpicture}
#+end_src

#+results:
[[file:tree.png]]

* COMMENT setup
#+begin_src emacs-lisp :results silent
  (setq org-babel-latex-htlatex "htlatex")
  (defmacro by-backend (&rest body)
    `(case org-export-current-backend ,@body))
#+end_src
--8<---------------cut here---------------end--------------->8---

The header line that says to use the package tikz right before the
source block is only necessary to generate the png when evaluating the
block (“C-c C-c” on it), but as it does not prevent the export to work,
I leave it there.

I had to change my systems pgfsys-tex4ht.def as described in
http://tex.stackexchange.com/questions/185349/error-using-pgfsysdriver-with-tex4ht-only-shows-up-with-texlive-2014-ok-with-t/232739#232739
(having a local copy and modifying it as suggested on the site did not
work).

Thanks again,

Alan

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