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 A240020 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma(2n-1). 4
 1, 2, 2, 3, 3, 4, 4, 5, 3, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 5, 5, 11, 12, 12, 13, 5, 13, 14, 6, 6, 14, 15, 15, 16, 16, 17, 7, 7, 17, 18, 12, 18, 19, 19, 20, 8, 8, 20, 21, 21, 22, 22, 23, 32, 23, 24, 24, 25, 7, 25, 26, 10, 10, 26, 27, 27, 28, 8, 8, 28, 29, 11, 11, 29, 30, 30, 31, 31, 32, 12, 26, 12, 32, 33, 9, 9, 33, 34, 34 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n lists the parts of the symmetric representation of A008438(n-1). Also these are the parts from the odd-indexed rows of A237270. Also these are the parts in the quadrants 1 and 3 of the spiral described in A239660, see example. Row sums give A008438. The length of row n is A237271(2n-1). Both column 1 and the right border are equal to n. Note that also the sequence can be represented in a quadrant. We can find the spiral (mentioned above) on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016 LINKS EXAMPLE 1; 2, 2; 3, 3; 4, 4; 5, 3, 5; 6, 6; 7, 7; 8, 8, 8; 9, 9; 10, 10; 11, 5, 5, 11; 12, 12; 13, 5, 13; 14, 6, 6, 14; 15, 15; 16, 16; 17, 7, 7, 17; 18, 12, 18; 19, 19; 20, 8, 8, 20; 21, 21; 22, 22; 23, 32, 23; 24, 24; 25, 7, 25; ... Illustration of initial terms (rows 1..8): . .                                   _ _ _ _ _ _ _ 7 .                                  |_ _ _ _ _ _ _| .                                                | .                                                |_ _ .                                   _ _ _ _ _ 5      |_ .                                  |_ _ _ _ _|         | .                                            |_ _ 3    |_ _ _ 7 .                                            |_  |         | | .                                   _ _ _ 3    |_|_ _ 5    | | .                                  |_ _ _|         | |     | | .                                        |_ _ 3    | |     | | .                                          | |     | |     | | .                                   _ 1    | |     | |     | | .     _       _       _       _    |_|     |_|     |_|     |_| .    | |     | |     | |     | | .    | |     | |     | |     |_|_ _ .    | |     | |     | |    2  |_ _| .    | |     | |     |_|_     2 .    | |     | |    4    |_ .    | |     |_|_ _        |_ _ _ _ .    | |    6      |_      |_ _ _ _| .    |_|_ _ _        |_   4 .   8      | |_ _      | .          |_    |     |_ _ _ _ _ _ .            |_  |_    |_ _ _ _ _ _| .           8  |_ _|  6 .                  | .                  |_ _ _ _ _ _ _ _ .                  |_ _ _ _ _ _ _ _| .                 8 . The figure shows the quadrants 1 and 3 of the spiral described in A239660. For n = 5 we have that 2*5 - 1 = 9 and the 9th row of A237593 is [5, 2, 2, 2, 2, 5] and the 8th row of A237593 is [5, 2, 1, 1, 2, 5] therefore between both symmetric Dyck paths there are three regions (or parts) of sizes [5, 3, 5], so row 5 is [5, 3, 5], see the third arm of the spiral in the first quadrant. The sum of divisors of 9 is 1 + 3 + 9 = A000203(9) = 13. On the other hand the sum of the parts of the symmetric representation of sigma(9) is 5 + 3 + 5 = 13, equaling the sum of divisors of 9. CROSSREFS Cf. A000203, A005408, A008438, A112610, A196020, A236104, A237048, A237270, A237271, A237591, A237593, A239053, A239660, A239931, A239933, A244050, A245092, A262626. Sequence in context: A220032 A219773 A187446 * A336430 A167232 A319468 Adjacent sequences:  A240017 A240018 A240019 * A240021 A240022 A240023 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Mar 31 2014 STATUS approved

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Last modified January 20 06:12 EST 2022. Contains 350467 sequences. (Running on oeis4.)