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 'Hindenburg order'. The term '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]]
[2,4] <-> [[2],[1,1]]
[3,9,21] <-> [[3],[1,2],[1,1,1]]
[4,16,12,56,156] <-> [[4],[1,3],[2,2],[1,1,2],[1,1,1,1]]
MAPLE
a := proc(n) local rev, P, R, i, l, s, k, j;
rev := l -> [seq(l[nops(l)-j+1], j=1..nops(l))];
P := rev(combinat[partition](n)); R := NULL;
for i to nops(P) do l := convert(P[i], 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