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 A379633 #23 Jan 07 2025 10:13:40 %S A379633 1,2,3,2,4,5,3,6,3,7,4,8,9,5,4,10,4,11,6,12,5,13,7,14,5,15,8,6,5,16, %T A379633 17,9,18,7,6,19,10,20,6,21,11,8,6,22,7,23,12,24,9,25,13,7,26,8,27,14, %U A379633 10,7,28,7,29,15,30,11,9,8,31,16,32,33,17,12,8,34,10,35,18,9,8,36,13,8,37,19,38,11,39,20,14,9,40,10,41,21 %N A379633 Irregular triangle read by rows in which row n lists the largest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts). %C A379633 Row n gives the first A001227(n) terms of the n-th row of A379631. %C A379633 Conjecture: the right border gives A212652. %e A379633 Triangle begins: %e A379633 1; %e A379633 2; %e A379633 3, 2; %e A379633 4; %e A379633 5, 3; %e A379633 6, 3; %e A379633 7, 4; %e A379633 8; %e A379633 9, 5, 4; %e A379633 10, 4; %e A379633 11, 6; %e A379633 12, 5; %e A379633 13, 7; %e A379633 14, 5; %e A379633 15, 8, 6, 5; %e A379633 16; %e A379633 17, 9; %e A379633 18, 7, 6; %e A379633 19, 10; %e A379633 20, 6; %e A379633 21, 11, 8, 6; %e A379633 22, 7; %e A379633 23, 12; %e A379633 24, 9; %e A379633 25, 13, 7; %e A379633 26, 8; %e A379633 27, 14, 10, 7; %e A379633 28, 7; %e A379633 ... %e A379633 Illustration of initial terms: %e A379633 _ %e A379633 _|1| %e A379633 _|2 _| %e A379633 _|3 |2| %e A379633 _|4 _| | %e A379633 _|5 |3 _| %e A379633 _|6 _| |3| %e A379633 _|7 |4 | | %e A379633 _|8 _| _| | %e A379633 _|9 |5 |4 _| %e A379633 _|10 _| | |4| %e A379633 _|11 |6 _| | | %e A379633 _|12 _| |5 | | %e A379633 _|13 |7 | _| | %e A379633 _|14 _| _| |5 _| %e A379633 _|15 |8 |6 | |5| %e A379633 _|16 _| | | | | %e A379633 _|17 |9 _| _| | | %e A379633 _|18 _| |7 |6 | | %e A379633 _|19 |10 | | _| | %e A379633 _|20 _| _| | |6 _| %e A379633 _|21 |11 |8 _| | |6| %e A379633 _|22 _| | |7 | | | %e A379633 _|23 |12 _| | | | | %e A379633 _|24 _| |9 | _| | | %e A379633 _|25 |13 | _| |7 | | %e A379633 _|26 _| _| |8 | _| | %e A379633 _|27 |14 |10 | | |7 _| %e A379633 |28 | | | | | |7| %e A379633 ... %e A379633 The diagram is also the left part of the diagram of A379631. %e A379633 The geometrical structure is the same as the diagram of A237591. %Y A379633 Positive terms of A286013. %Y A379633 Column 1 gives A000027. %Y A379633 Row lengths give A001227. %Y A379633 Row sums give A286015. %Y A379633 Subsequence of A286000 and of A299765 and of A379631. %Y A379633 For the smallest parts see A379632. %Y A379633 Cf. A196020, A212652, A235791, A236104, A237048, A237591, A237593, A245092, A262626, A379630, A379634. %K A379633 nonn,tabf %O A379633 1,2 %A A379633 _Omar E. Pol_, Dec 31 2024