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 A239932 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-2). 17
 3, 12, 9, 9, 12, 12, 39, 18, 18, 21, 21, 72, 27, 27, 30, 30, 96, 36, 36, 39, 15, 39, 120, 45, 45, 48, 48, 144, 54, 36, 54, 57, 57, 84, 84, 63, 63, 66, 66, 234, 72, 72, 75, 21, 75, 108, 108, 81, 81, 84, 48, 84, 120, 120, 90, 90, 93, 93, 312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row n is a palindromic composition of sigma(4n-2). Row n is also the row 4n-2 of A237270. Row n has length A237271(4n-2). Row sums give A239052. Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the second quadrant of the spiral described in A239660, see example. For the parts of the symmetric representation of sigma(4n-3), see A239931. For the parts of the symmetric representation of sigma(4n-1), see A239933. For the parts of the symmetric representation of sigma(4n), see A239934. We can find the spiral (mentioned above) on the terraces of the pyramid described in A244050. - Omar E. Pol, Dec 06 2016 LINKS EXAMPLE The irregular triangle begins: 3; 12; 9, 9; 12, 12; 39; 18, 18; 21, 21; 72; 27, 27; 30, 30; 96; 36, 36; 39, 15, 39; 120; 45, 45; 48, 48; ... Illustration of initial terms in the second quadrant of the spiral described in A239660: .                                 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .                                |  _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| .                                | | .                                | | .                                | |  _ _ _ _ _ _ _ _ _ _ _ _ _ _ .                           _ _ _| | |  _ _ _ _ _ _ _ _ _ _ _ _ _| .                          |       | | | .                       _ _|  _ _ _| | | .                  72 _|     |       | |  _ _ _ _ _ _ _ _ _ _ _ _ .                   _|      _| 21 _ _| | |  _ _ _ _ _ _ _ _ _ _ _| .                  |      _|     |_ _ _| | | .               _ _|    _|    _ _|       | | .              |    _ _|    _|     18 _ _| |  _ _ _ _ _ _ _ _ _ _ .              |   |       |         |_ _ _| |  _ _ _ _ _ _ _ _ _| .     _ _ _ _ _|   | 21 _ _|        _|       | | .    |  _ _ _ _ _ _|   | |        _|      _ _| | .    | |      _ _ _ _ _| | 18 _ _|       |     |  _ _ _ _ _ _ _ _ .    | |     |  _ _ _ _ _|   | |     39 _|  _ _| |  _ _ _ _ _ _ _| .    | |     | |      _ _ _ _| |    _ _|  _|     | | .    | |     | |     |  _ _ _ _|   |    _|   12 _| | .    | |     | |     | |      _ _ _|   |       |_ _|  _ _ _ _ _ _ .    | |     | |     | |     |  _ _ _ _| 12 _ _|     |  _ _ _ _ _| .    | |     | |     | |     | |      _ _ _| |    9 _| | .    | |     | |     | |     | |     |  _ _ _|  9 _|_ _| .    | |     | |     | |     | |     | |      _ _| |      _ _ _ _ .    | |     | |     | |     | |     | |     |  _ _| 12 _|  _ _ _| .    | |     | |     | |     | |     | |     | |      _|   | .    | |     | |     | |     | |     | |     | |     |  _ _| .    | |     | |     | |     | |     | |     | |     | |    3 _ _ .    | |     | |     | |     | |     | |     | |     | |     |  _| .    |_|     |_|     |_|     |_|     |_|     |_|     |_|     |_| . For n = 7 we have that 4*7-2 = 26 and the 26th row of A237593 is [14, 5, 2, 2, 2, 1, 1, 2, 2, 2, 5, 14] and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] therefore between both Dyck paths there are two regions (or parts) of sizes [21, 21], so row 7 is [21, 21]. The sum of divisors of 26 is 1 + 2 + 13 + 26 = A000203(26) = 42. On the other hand the sum of the parts of the symmetric representation of sigma(26) is 21 + 21 = 42, equaling the sum of divisors of 26. CROSSREFS Cf. A000203, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239052, A239660, A239931, A239933, A239934, A244050, A245092, A262626. Sequence in context: A234947 A051353 A070706 * A114237 A060035 A165988 Adjacent sequences:  A239929 A239930 A239931 * A239933 A239934 A239935 KEYWORD nonn,tabf,more AUTHOR Omar E. Pol, Mar 29 2014 STATUS approved

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)