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%I #23 Oct 21 2020 03:47:13
%S 1,2,11,3,21,111,4,31,22,211,1111,5,41,32,311,221,2111,11111,6,51,42,
%T 411,33,321,3111,222,2211,21111,111111,7,61,52,511,43,421,4111,331,
%U 322,3211,31111,2221,22111,211111,1111111
%N Irregular triangle read by rows in which n-th row lists all partitions of n, in graded reverse lexicographic ordering, using a compressed notation.
%C Officially this is deprecated, since one cannot distinguish between (for example) parts which are 11 and parts which are 1,1. However, it is in common use and is included for completeness. See A036037, A080577, etc., for uncompressed versions.
%H Alois P. Heinz, <a href="/A322761/b322761.txt">Rows n = 1..28, flattened</a>
%e Triangle begins:
%e 1,
%e 2, 11,
%e 3, 21, 111,
%e 4, 31, 22, 211, 1111,
%e 5, 41, 32, 311, 221, 2111, 11111,
%e 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111,
%e 7, 61, 52, 511, 43, 421, 4111, 331, 322, 3211, 31111, 2221, 22111, 211111, 1111111,
%e ...
%e ...
%p b:= (n, i)-> `if`(n=0 or i=1, [cat(1$n)], [map(x->
%p cat(i, x), b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
%p T:= n-> map(parse, b(n$2))[]:
%p seq(T(n), n=1..10); # _Alois P. Heinz_, Dec 30 2018
%t revlexsort[f_, c_] := OrderedQ[PadRight[{c, f}]];
%t Table[FromDigits /@ Sort[IntegerPartitions[n], revlexsort], {n, 1, 8}] // Flatten (* _Jean-François Alcover_, Oct 20 2020, after _Gus Wiseman_ in A080577 *)
%Y Cf. A000041 (number of terms in row n), A036037, A080577.
%Y See also A006128.
%Y First column gives A000027.
%Y Last elements of rows give A000042.
%K nonn,look,tabf,base,fini
%O 1,2
%A _N. J. A. Sloane_, Dec 30 2018
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