A157407 The integer partitions of n taken as digits in base n+1 and listed in the reflected Hindenburg order.

0, 1, 4, 2, 21, 6, 3, 156, 32, 12, 8, 4, 1555, 260, 50, 45, 15, 10, 5, 19608, 2802, 408, 114, 402, 66, 24, 60, 18, 12, 6, 299593, 37450, 4690, 658, 4683, 595, 147, 91, 588, 84, 28, 77, 21, 14, 7

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).

The offset of row n (n>0) is A000070[n+1], the length of row n is A000041[n]. The left 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]]
[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

Cf. A157406

Sequence in context: A354094 A347590 A016517 * A100400 A285439 A336598

Adjacent sequences: A157404 A157405 A157406 * A157408 A157409 A157410

Keyword

easy,nonn,tabf,base

Author

Peter Luschny, Mar 11 2009

Status

approved