This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A239665 #59 Jul 24 2018 09:46:26 %S A239665 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 A239665 29,61,179,452,152,68,32,32,68,152,452,1250,418,182,152,100,152,182, %U A239665 418,1250,3035,1013,437,342,85,85,342,437,1013,3035,6958,1394,638,314,154,236,154,314,638,1394,6958 %N 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. %C A239665 Row n is also row A239663(n) of A237270. %e A239665 ---------------------------------------------------------------------- %e A239665 n A239663(n) Triangle begins: A266094(n) %e A239665 ---------------------------------------------------------------------- %e A239665 1 1 [1] 1 %e A239665 2 3 [2, 2] 4 %e A239665 3 9 [5, 3, 5] 13 %e A239665 4 21 [11, 5, 5, 11] 32 %e A239665 5 63 [32, 12, 16, 12, 32] 104 %e A239665 6 147 [74, 26, 14, 14, 26, 74] 228 %e A239665 7 357 [179, 61, 29, 38, 29, 61, 179] 576 %e A239665 8 903 [452, 152, 68, 32, 32, 68, 152, 452] 1408 %e A239665 ... %e A239665 Illustration of initial terms: %e A239665 . %e A239665 . _ _ _ _ _ 5 %e A239665 . |_ _ _ _ _| %e A239665 . |_ _ 3 %e A239665 . |_ | %e A239665 . |_|_ _ 5 %e A239665 . | | %e A239665 . _ _ 2 | | %e A239665 . |_ _|_ 2 | | %e A239665 . _ 1| | | | %e A239665 . |_| |_| |_| %e A239665 . %e A239665 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 A239665 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 A239665 Cf. A000203, A005279, A196020, A236104, A237270, A237271, A235791, A237591, A237593, A239660, A239663, A239931-A239934, A240020, A240062, A244050, A245092, A262626, A266094. %K A239665 nonn,tabl %O A239665 1,2 %A A239665 _Omar E. Pol_, Mar 23 2014 %E A239665 a(16)-a(28) from _Michel Marcus_ and _Omar E. Pol_, Mar 28 2014 %E A239665 a(29)-a(36) from _Michel Marcus_, Mar 28 2014 %E A239665 a(37)-a(45) from _Michel Marcus_, Mar 29 2014 %E A239665 a(46)-a(66) from _Michel Marcus_, Apr 02 2014