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A049085
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Maximal part of partition described in A036043.
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7
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1, 2, 1, 3, 2, 1, 4, 3, 2, 2, 1, 5, 4, 3, 3, 2, 2, 1, 6, 5, 4, 3, 4, 3, 2, 3, 2, 2, 1, 7, 6, 5, 4, 5, 4, 3, 3, 4, 3, 2, 3, 2, 2, 1, 8, 7, 6, 5, 4, 6, 5, 4, 4, 3, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1, 9, 8, 7, 6, 5, 7, 6, 5, 4, 5, 4, 3, 6, 5, 4, 4, 3, 3, 5, 4, 3, 3, 2, 4, 3, 2, 3, 2, 2, 1, 10, 9, 8, 7, 6, 5, 8, 7, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Like A036043 this is important for calculating sequences defined over the numeric partitions, cf. A000041. For example, the triangular array A019575 can be calculated using A036042 and a(n).
The sequence of the row lengths of this array is A000041(n), n>=1 (partition numbers). - W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 28 2005
The row sums are A006128. [From Johannes W. Meijer (meijgia(AT)hotmail.com), June 21, 2010]
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
W. Lang: First 15 rows.
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EXAMPLE
| Rows: [1]; [2,1]; [3,2,1]; [4,3,2,2,1]; [5,4,3,3,2,2,1]; ...
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MAPLE
| with(combinat): nmax:=9: for n from 1 to nmax do y(n):=numbpart(n): P(n):=partition(n): for k from 1 to y(n) do B(k):=P(n)[k] od: for k from 1 to y(n) do s:=0: j:=0: while s<n do j:=j+1: s:=s+B(k)[j]: Q(n, k):=j; end do: od: od: T:=0: for n from 1 to nmax do for j from 1 to numbpart(n) do T:=T+1: a(T):= Q(n, j) od; od: seq(a(n), n=1..T); [From Johannes W. Meijer (meijgia(AT)hotmail.com), June 21, 2010]
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CROSSREFS
| Cf. A036042, A036043, A000041.
Sequence in context: A200082 A052310 A052313 * A193173 A167287 A007336
Adjacent sequences: A049082 A049083 A049084 * A049086 A049087 A049088
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KEYWORD
| nice,nonn,tabf
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
| More terms from W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 28 2005
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