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Triangle read by rows: row n lists all partitions of n in the order produced by the shell model of partitions A138151.
6

%I #11 May 28 2020 21:36:41

%S 1,2,1,1,3,2,1,1,1,1,4,2,2,3,1,2,1,1,1,1,1,1,5,3,2,4,1,2,2,1,3,1,1,2,

%T 1,1,1,1,1,1,1,1,6,4,2,3,3,2,2,2,5,1,3,2,1,4,1,1,2,2,1,1,3,1,1,1,2,1,

%U 1,1,1,1,1,1,1,1,1,7,5,2,4,3,3,2,2,6,1,4,2,1,3,3,1,2,2,2,1,5,1,1,3,2,1,1,4

%N Triangle read by rows: row n lists all partitions of n in the order produced by the shell model of partitions A138151.

%C See the integrated diagram of partitions in the entry A138138.

%C See A138151 for more information.

%C First 43 members = A026792.

%H Robert Price, <a href="/A139100/b139100.txt">Table of n, a(n) for n = 1..7043, 17 rows.</a>

%e Triangle begins:

%e {(1)}

%e {(2), (1, 1)}

%e {(3), (2, 1), (1, 1, 1)}

%e {(4), (2, 2), (3, 1), (2, 1, 1), (1, 1, 1, 1)}

%e {(5), (3, 2), (4, 1), (2, 2, 1), (3, 1, 1), (2, 1, 1, 1), (1, 1, 1, 1, 1)}

%t Table[If[n == 1, ConstantArray[{1}, i - n + 1],

%t Map[(Join[#, ConstantArray[{1}, i - n]]) &,

%t Cases[IntegerPartitions[n], x_ /; Last[x] != 1]]], {i, 7}, {n, i, 1, -1}] // Flatten(* _Robert Price_, May 28 2020 *)

%Y Cf. A000041, A006128, A026792, A036036, A080576, A080577, A135010, A138121, A138135, A138136, A138137, A138138, A138151.

%K nonn,tabf,less

%O 1,2

%A _Omar E. Pol_, Apr 15 2008