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%I #59 Jul 24 2018 09:46:26
%S 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,
%T 29,61,179,452,152,68,32,32,68,152,452,1250,418,182,152,100,152,182,
%U 418,1250,3035,1013,437,342,85,85,342,437,1013,3035,6958,1394,638,314,154,236,154,314,638,1394,6958
%N 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.
%C Row n is also row A239663(n) of A237270.
%e ----------------------------------------------------------------------
%e n A239663(n) Triangle begins: A266094(n)
%e ----------------------------------------------------------------------
%e 1 1 [1] 1
%e 2 3 [2, 2] 4
%e 3 9 [5, 3, 5] 13
%e 4 21 [11, 5, 5, 11] 32
%e 5 63 [32, 12, 16, 12, 32] 104
%e 6 147 [74, 26, 14, 14, 26, 74] 228
%e 7 357 [179, 61, 29, 38, 29, 61, 179] 576
%e 8 903 [452, 152, 68, 32, 32, 68, 152, 452] 1408
%e ...
%e Illustration of initial terms:
%e .
%e . _ _ _ _ _ 5
%e . |_ _ _ _ _|
%e . |_ _ 3
%e . |_ |
%e . |_|_ _ 5
%e . | |
%e . _ _ 2 | |
%e . |_ _|_ 2 | |
%e . _ 1| | | |
%e . |_| |_| |_|
%e .
%e 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].
%e 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].
%Y Cf. A000203, A005279, A196020, A236104, A237270, A237271, A235791, A237591, A237593, A239660, A239663, A239931-A239934, A240020, A240062, A244050, A245092, A262626, A266094.
%K nonn,tabl
%O 1,2
%A _Omar E. Pol_, Mar 23 2014
%E a(16)-a(28) from _Michel Marcus_ and _Omar E. Pol_, Mar 28 2014
%E a(29)-a(36) from _Michel Marcus_, Mar 28 2014
%E a(37)-a(45) from _Michel Marcus_, Mar 29 2014
%E a(46)-a(66) from _Michel Marcus_, Apr 02 2014
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