A239665 Triangle read by rows in which row n lists the parts of the symmetric representation of sigma of the smallest number whose symmetric representation of sigma has n parts.

1, 2, 2, 5, 3, 5, 11, 5, 5, 11, 32, 12, 16, 12, 32, 74, 26, 14, 14, 26, 74, 179, 61, 29, 38, 29, 61, 179, 452, 152, 68, 32, 32, 68, 152, 452, 1250, 418, 182, 152, 100, 152, 182, 418, 1250, 3035, 1013, 437, 342, 85, 85, 342, 437, 1013, 3035, 6958, 1394, 638, 314, 154, 236, 154, 314, 638, 1394, 6958

Offset

1,2

Comments

Row n is also row A239663(n) of A237270.

Links

Table of n, a(n) for n=1..66.

Example

----------------------------------------------------------------------
n    A239663(n)  Triangle begins:                        A266094(n)
----------------------------------------------------------------------
1        1       [1]                                         1
2        3       [2, 2]                                      4
3        9       [5, 3, 5]                                  13
4       21       [11, 5, 5, 11]                             32
5       63       [32, 12, 16, 12, 32]                      104
6      147       [74, 26, 14, 14, 26, 74]                  228
7      357       [179, 61, 29, 38, 29, 61, 179]            576
8      903       [452, 152, 68, 32, 32, 68, 152, 452]     1408
...
Illustration of initial terms:
.
.     _ _ _ _ _ 5
.    |_ _ _ _ _|
.              |_ _ 3
.              |_  |
.                |_|_ _ 5
.                    | |
.     _ _ 2          | |
.    |_ _|_ 2        | |
.     _ 1| |         | |
.    |_| |_|         |_|
.
For n = 2 we have that A239663(2) = 3 is the smallest number whose symmetric representation of sigma has 2 parts. Row 3 of A237593 is [2, 1, 1, 2] and row 2 of A237593 is [2, 2] therefore between both Dyck paths in the first quadrant there are two regions (or parts) of sizes [2, 2], so row 2 is [2, 2].
For n = 3 we have that A239663(3) = 9 is the smallest number whose symmetric representation of sigma has 3 parts. 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 Dyck paths in the first quadrant there are three regions (or parts) of sizes [5, 3, 5], so row 3 is [5, 3, 5].

Crossrefs

Cf. A000203, A005279, A196020, A236104, A237270, A237271, A235791, A237591, A237593, A239660, A239663, A239931-A239934, A240020, A240062, A244050, A245092, A262626, A266094.

Sequence in context: A341443 A224166 A286109 * A178179 A284833 A321202

Adjacent sequences: A239662 A239663 A239664 * A239666 A239667 A239668

Keyword

nonn,tabl

Author

Omar E. Pol, Mar 23 2014

Extensions

a(16)-a(28) from Michel Marcus and Omar E. Pol, Mar 28 2014

a(29)-a(36) from Michel Marcus, Mar 28 2014

a(37)-a(45) from Michel Marcus, Mar 29 2014

a(46)-a(66) from Michel Marcus, Apr 02 2014

Status

approved