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A139100 Triangle read by rows: row n lists all partitions of n in the order produced by the shell model of partitions A138151.

%I A139100 #11 May 28 2020 21:36:41
%S A139100 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 A139100 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 A139100 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 A139100 Triangle read by rows: row n lists all partitions of n in the order produced by the shell model of partitions A138151.
%C A139100 See the integrated diagram of partitions in the entry A138138.
%C A139100 See A138151 for more information.
%C A139100 First 43 members = A026792.
%H A139100 Robert Price, <a href="/A139100/b139100.txt">Table of n, a(n) for n = 1..7043, 17 rows.</a>
%e A139100 Triangle begins:
%e A139100 {(1)}
%e A139100 {(2), (1, 1)}
%e A139100 {(3), (2, 1), (1, 1, 1)}
%e A139100 {(4), (2, 2), (3, 1), (2, 1, 1), (1, 1, 1, 1)}
%e A139100 {(5), (3, 2), (4, 1), (2, 2, 1), (3, 1, 1), (2, 1, 1, 1), (1, 1, 1, 1, 1)}
%t A139100 Table[If[n == 1, ConstantArray[{1}, i - n + 1],
%t A139100    Map[(Join[#, ConstantArray[{1}, i - n]]) &,
%t A139100     Cases[IntegerPartitions[n], x_ /; Last[x] != 1]]], {i, 7}, {n, i, 1, -1}]  // Flatten(* _Robert Price_, May 28 2020 *)
%Y A139100 Cf. A000041, A006128, A026792, A036036, A080576, A080577, A135010, A138121, A138135, A138136, A138137, A138138, A138151.
%K A139100 nonn,tabf,less
%O A139100 1,2
%A A139100 _Omar E. Pol_, Apr 15 2008