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Search: id:A157406
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| A157406 |
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The integer partitions of n taken as digits in base n+1 and listed in the Hindenburg order. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
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LINKS
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Peter Luschny, Counting with Partitions.
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EXAMPLE
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[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]]
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MAPLE
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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)];
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CROSSREFS
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Cf. A157407
Sequence in context: A096901 A100781 A110339 this_sequence A075363 A082382 A064691
Adjacent sequences: A157403 A157404 A157405 this_sequence A157407 A157408 A157409
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Mar 11 2009
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