OFFSET
0,3
COMMENTS
The rows are enumerated 0,1,2,... Converting the numbers in the n-th row (n>0) to base n+1 gives all partitions of n in the 'reflected Hindenburg order'. The term 'reflected Hindenburg order' is not standard and refers to the partition generating algorithm of C. F. Hindenburg (1779).
LINKS
Peter Luschny, Counting with Partitions.
EXAMPLE
[0] <-> [[ ]]
[1] <-> [[1]]
[4,2] <-> [[1,1],[2]]
[21,6,3] <-> [[1,1,1],[2,1],[3]]
[156,32,12,8,4] <-> [[1,1,1,1],[2,1,1],[2,2],[3,1],[4]]
MAPLE
a := proc(n) local rev, P, R, Q, i, l, s, k, j;
rev := l -> [seq(l[nops(l)-j+1], j=1..nops(l))];
P := combinat[partition](n); R := NULL;
for i to nops(P) do Q := rev(P[i]);
l := convert(Q, base, n+1, 10);
s := add(l[k]*10^(k-1), k=1..nops(l));
R:= R, s; od; R end: [0, seq(a(i), i=1..7)];
CROSSREFS
KEYWORD
easy,nonn,tabf,base
AUTHOR
Peter Luschny, Mar 11 2009
STATUS
approved