Created:  July 2011

                         Previous version of  Feb. 2013

                         This version: Sept. 30, 2015.



                                This is Cfinite

                          It accompanyies the article

                       The Algebra of C-finite Sequences

                              by Doron Zeilberger

                 dedicatd to Mourad Ismail and Dennis Stanton.

                  and also available from Zeilberger's website



           Please report bugs to zeilberg at math dot rutgers dot edu



              The most current version of this  package and paper

                               are  available from

                   http://www.math.rutgers.edu/~zeilberg/  .

                            -----------------------

      For a list of the Story procedures type ezraStory();, for help with

              a specific procedure, type ezra(procedure_name);   .



                        -------------------------------

                            -----------------------

           For a list of the procedures coding famous sequences, type

                                 ezraFamous();

                                  for help with

              a specific procedure, type ezra(procedure_name);   .



                        -------------------------------

                            -----------------------

      For a list of the supporting procedures type ezra1();, for help with

              a specific procedure, type ezra(procedure_name);   .



                        -------------------------------

                            -----------------------

         For a list of the MAIN procedures type ezra();, for help with

              a specific procedure, type ezra(procedure_name);   .



                         ------------------------------

The first, 10, terms of the sequences of words in {1,...n} with, r,

    occurrences of each letter, avoiding the pattern 1234

    and the pattern 1k(k-1)...2 for r from 1 to, 2, and for k from 3 to , 5



                            By Yonah B-A's computer





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The first, 10,

    terms of the sequence enumerating the number of words in {1,...n} with, 1,

    occurrences of each letter

              avoiding the pattern 1234 and the pattern, 132, are



                  [1, 2, 5, 13, 34, 89, 233, 610, 1597, 4181]



                               The time is, 0.026





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The first, 10,

    terms of the sequence enumerating the number of words in {1,...n} with, 2,

    occurrences of each letter

              avoiding the pattern 1234 and the pattern, 132, are



         [1, 6, 43, 290, 1894, 12219, 78368, 501124, 3197562, 20383754]



                               The time is, 1.147





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The first, 10,

    terms of the sequence enumerating the number of words in {1,...n} with, 1,

    occurrences of each letter

             avoiding the pattern 1234 and the pattern, 1432, are



                [1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382]



                               The time is, 2.692





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The first, 10,

    terms of the sequence enumerating the number of words in {1,...n} with, 2,

    occurrences of each letter

             avoiding the pattern 1234 and the pattern, 1432, are



   [1, 6, 90, 1428, 21386, 311364, 4470737, 63753284, 905764059, 12841256477]



                             The time is, 6976.405





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                  -------------------------------------------



The first, 10,

    terms of the sequence enumerating the number of words in {1,...n} with, 1,

    occurrences of each letter

             avoiding the pattern 1234 and the pattern, 15432, are



              [1, 2, 6, 23, 102, 487, 2403, 12021, 60470, 304862]



                             The time is, 7043.357





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