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
Examples
---------------------------------------------------------------------- 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
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
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