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Search: id:A145573
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| A145573 |
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Characteristic partition array for partitions without part 1. |
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+0
2
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| 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The partitions are ordered according to Abramowitz-Stegun (A-St order). See e.g. A036040 for the reference, pp. 831-2.
The row lengths of this array are p(n)=A000041(n) (number of partitions of n).
The entries of row n are grouped together for partitions with rising parts number m from 1 to n. The number of partitions of n with m parts is p(n,m)= A008284(n,m), m=1..n, n>=1.
For the array without zeros see A145574.
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LINKS
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W. Lang, M. Sjodahl First 10 rows of the array and row sums.
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FORMULA
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As array: a(n,k)=1 if the kth partition of n in A-St order has no part 1, and a(n,k)=0 else.
Translated into the sequence a(m) entry: a(n,k) = a(sum(p(k),k=1..n)+k).
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EXAMPLE
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[0],[1,0],[1,0,0],[1,0,1,0,0],[1,0,1,0,0,0,0],...
a(4,3) = a(1+2+3+3) = a(9) = 1 because a(4,3) belongs to the partition [2^2]=[2,2] of n=4 which has no part 1.
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CROSSREFS
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Cf. A145574 (without zeros). A002865 (row sums).
Sequence in context: A141474 A073424 A135993 this_sequence A092202 A159684 A163538
Adjacent sequences: A145570 A145571 A145572 this_sequence A145574 A145575 A145576
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) and Malin Sjodahl (malin.sjodahl(AT)physik.uni-karlsruhe.de) Mar 06 2009
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