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 A239931 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(4n-3). 46
 1, 3, 3, 5, 3, 5, 7, 7, 9, 9, 11, 5, 5, 11, 13, 5, 13, 15, 15, 17, 7, 7, 17, 19, 19, 21, 21, 23, 32, 23, 25, 7, 25, 27, 27, 29, 11, 11, 29, 31, 31, 33, 9, 9, 33, 35, 13, 13, 35, 37, 37, 39, 18, 39, 41, 15, 9, 15, 41, 43, 11, 11, 43, 45, 45, 47, 17, 17, 47, 49, 49, 51, 51, 53, 43, 43, 53, 55, 55, 57, 57, 59, 21, 22, 21, 59, 61, 11, 61, 63, 15, 15, 63 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n is a palindromic composition of sigma(4n-3). Row n is also the row 4n-3 of A237270. Row n has length A237271(4n-3). Row sums give A112610. Also row n lists the parts of the symmetric representation of sigma in the n-th arm of the first quadrant of the spiral described in A239660, see example. For the parts of the symmetric representation of sigma(4n-2), see A239932. 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:    1;    3,  3;    5,  3,  5;    7,  7;    9,  9;   11,  5,  5, 11;   13,  5, 13;   15, 15;   17,  7,  7, 17;   19, 19;   21, 21;   23, 32, 23;   25,  7, 25;   27, 27;   29, 11, 11, 29;   31, 31;   ... Illustration of initial terms in the first quadrant of the spiral described in A239660: . .     _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15 .    |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| .                                  | .                                  | .     _ _ _ _ _ _ _ _ _ _ _ _ _ 13 | .    |_ _ _ _ _ _ _ _ _ _ _ _ _|   | .                              |   |_ _ _ .                              |         | .     _ _ _ _ _ _ _ _ _ _ _ 11 |         |_ .    |_ _ _ _ _ _ _ _ _ _ _|   |_ _ _      |_ .                          |         |_ _ 5  |_ .                          |         |_  |_    |_ _ .     _ _ _ _ _ _ _ _ _ 9  |_ _ _      |_  |       | .    |_ _ _ _ _ _ _ _ _|   |_ _  |_ 5    |_|_      | .                      |       |_ _|_ 5      |     |_ _ _ _ _ _ 15 .                      |           | |_      |               | | .     _ _ _ _ _ _ _ 7  |_ _        |_  |     |_ _ _ _ _ 13   | | .    |_ _ _ _ _ _ _|       |_        | |             | |     | | .                  |         |_      |_|_ _ _ _ 11   | |     | | .                  |_ _        |             | |     | |     | | .     _ _ _ _ _ 5      |_      |_ _ _ _ 9    | |     | |     | | .    |_ _ _ _ _|         |           | |     | |     | |     | | .              |_ _ 3    |_ _ _ 7    | |     | |     | |     | | .              |_  |         | |     | |     | |     | |     | | .     _ _ _ 3    |_|_ _ 5    | |     | |     | |     | |     | | .    |_ _ _|         | |     | |     | |     | |     | |     | | .          |_ _ 3    | |     | |     | |     | |     | |     | | .            | |     | |     | |     | |     | |     | |     | | .     _ 1    | |     | |     | |     | |     | |     | |     | | .    |_|     |_|     |_|     |_|     |_|     |_|     |_|     |_| . For n = 7 we have that 4*7-3 = 25 and the 25th row of A237593 is [13, 5, 3, 1, 2, 1, 1, 2, 1, 3, 5, 13] and the 24th row of A237593 is [13, 4, 3, 2, 1, 1, 1, 1, 2, 3, 4, 13] therefore between both Dyck paths there are three regions (or parts) of sizes [13, 5, 13], so row 7 is [13, 5, 13]. The sum of divisors of 25 is 1 + 5 + 25 = A000203(25) = 31. On the other hand the sum of the parts of the symmetric representation of sigma(25) is 13 + 5 + 13 = 31, equaling the sum of divisors of 25. CROSSREFS Cf. A000203, A112610, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239932-A239934, A244050, A245092, A262626. Sequence in context: A255316 A078587 A335074 * A033558 A046217 A057662 Adjacent sequences:  A239928 A239929 A239930 * A239932 A239933 A239934 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Mar 29 2014 STATUS approved

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Last modified April 15 01:23 EDT 2021. Contains 342973 sequences. (Running on oeis4.)