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A322761
Irregular triangle read by rows in which n-th row lists all partitions of n, in graded reverse lexicographic ordering, using a compressed notation.
9
1, 2, 11, 3, 21, 111, 4, 31, 22, 211, 1111, 5, 41, 32, 311, 221, 2111, 11111, 6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111, 7, 61, 52, 511, 43, 421, 4111, 331, 322, 3211, 31111, 2221, 22111, 211111, 1111111
OFFSET
1,2
COMMENTS
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.
LINKS
EXAMPLE
Triangle begins:
1,
2, 11,
3, 21, 111,
4, 31, 22, 211, 1111,
5, 41, 32, 311, 221, 2111, 11111,
6, 51, 42, 411, 33, 321, 3111, 222, 2211, 21111, 111111,
7, 61, 52, 511, 43, 421, 4111, 331, 322, 3211, 31111, 2221, 22111, 211111, 1111111,
...
...
MAPLE
b:= (n, i)-> `if`(n=0 or i=1, [cat(1$n)], [map(x->
cat(i, x), b(n-i, min(n-i, i)))[], b(n, i-1)[]]):
T:= n-> map(parse, b(n$2))[]:
seq(T(n), n=1..10); # Alois P. Heinz, Dec 30 2018
MATHEMATICA
revlexsort[f_, c_] := OrderedQ[PadRight[{c, f}]];
Table[FromDigits /@ Sort[IntegerPartitions[n], revlexsort], {n, 1, 8}] // Flatten (* Jean-François Alcover, Oct 20 2020, after Gus Wiseman in A080577 *)
CROSSREFS
Cf. A000041 (number of terms in row n), A036037, A080577.
See also A006128.
First column gives A000027.
Last elements of rows give A000042.
Sequence in context: A127668 A261300 A068743 * A113736 A241596 A365769
KEYWORD
nonn,look,tabf,base,fini
AUTHOR
N. J. A. Sloane, Dec 30 2018
STATUS
approved