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 A339275 Irregular triangle read by rows: T(n,k), n >= 1, k >= 1, in which column k lists the terms of A040000: 1, 2, 2, 2, ... interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2. 3
 1, 2, 2, 1, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,k) is also the number of horizontal line segments in the n-th level of the k-th largest double-staircase of the diagram defined in A335616 (see example). The partial sums of column k give the k-th column of A338721. LINKS EXAMPLE Triangle begins (rows 1..28): 1; 2; 2,  1; 2,  0; 2,  2; 2,  0,  1; 2,  2,  0; 2,  0,  0; 2,  2,  2; 2,  0,  0,  1; 2,  2,  0,  0; 2,  0,  2,  0; 2,  2,  0,  0; 2,  0,  0,  2; 2,  2,  2,  0,  1; 2,  0,  0,  0,  0; 2,  2,  0,  0,  0; 2,  0,  2,  2,  0; 2,  2,  0,  0,  0; 2,  0,  0,  0,  2; 2,  2,  2,  0,  0,  1; 2,  0,  0,  2,  0,  0; 2,  2,  0,  0,  0,  0; 2,  0,  2,  0,  0,  0; 2,  2,  0,  0,  2,  0; 2,  0,  0,  2,  0,  0; 2,  2,  2,  0,  0,  2; 2,  0,  0,  0,  0,  0,  1; ... For an illustration of the rows of triangle consider the infinite "double-staircases" diagram defined in A335616. The first 15 levels of the structure looks like this: . Level                         "Double-staircases" diagram n                                          _ 1                                        _|1|_ 2                                      _|1 _ 1|_ 3                                    _|1  |1|  1|_ 4                                  _|1   _| |_   1|_ 5                                _|1    |1 _ 1|    1|_ 6                              _|1     _| |1| |_     1|_ 7                            _|1      |1  | |  1|      1|_ 8                          _|1       _|  _| |_  |_       1|_ 9                        _|1        |1  |1 _ 1|  1|        1|_ 10                     _|1         _|   | |1| |   |_         1|_ 11                   _|1          |1   _| | | |_   1|          1|_ 12                 _|1           _|   |1  | |  1|   |_           1|_ 13               _|1            |1    |  _| |_  |    1|            1|_ 14             _|1             _|    _| |1 _ 1| |_    |_             1|_ 15            |1              |1    |1  | |1| |  1|    1|              1| . For n = 15, in the 15th level of the diagram we have that the first largest double-staircase has two horizontal steps, the second double-staircase has two steps, the third double-staircase has two steps, there are no steps in the fourth double-stairce and the fifth double-staircase has only one step, so the 15th row of triangle is [2, 2, 2, 0, 1]. CROSSREFS Column 1 is A040000. Row sums give A335616. Row n has length A003056(n). Column k starts in row A000217(k). The number of positive terms in row n is A001227(n). Cf. A196020, A236104, A237048, A237270, A237591, A237593, A249351, A280850, A296508, A299484, A338721. Sequence in context: A156381 A089077 A203398 * A225064 A130071 A321373 Adjacent sequences:  A339272 A339273 A339274 * A339276 A339277 A339278 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Dec 01 2020 STATUS approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)