A157406 The integer partitions of n taken as digits in base n+1 and listed in the Hindenburg order.

0, 1, 2, 4, 3, 9, 21, 4, 16, 12, 56, 156, 5, 25, 20, 115, 85, 475, 1555, 6, 36, 30, 204, 24, 162, 1086, 114, 792, 5202, 19608, 7, 49, 42, 329, 35, 273, 2121, 217, 210, 1673, 12873, 1169, 9289, 70217, 299593

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).

The offset of row n (n>0) is A000070[n+1], the length of row n is A000041[n]. The right hand side of the triangle 0,1,4,21,156,... is A060072.

Links

Table of n, a(n) for n=0..44.

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

Cf. A157407

Sequence in context: A358488 A110339 A223703 * A075363 A082382 A239599

Adjacent sequences: A157403 A157404 A157405 * A157407 A157408 A157409

Keyword

easy,nonn,tabf,base

Author

Peter Luschny, Mar 11 2009

Status

approved