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A049085 Irregular table T(n,k) = maximal part of the k-th partition of n, when listed in Abramowitz-Stegun order (as in A036043). 8
0, 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; text; internal format)
OFFSET

0,3

COMMENTS

a(0) = 0 by convention. - Franklin T. Adams-Watters, Jun 24 2014

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 this sequence.

The row sums are A006128. - Johannes W. Meijer, Jun 21 2010

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.

LINKS

Alois P. Heinz, Rows n = 0..26, flattened

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.

EXAMPLE

Rows:

[0];

[1];

[2,1];

[3,2,1];

[4,3,2,2,1];

[5,4,3,3,2,2,1];

...

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:

0, seq(a(n), n=1..T); # Johannes W. Meijer, Jun 21 2010

PROG

(PARI) A049085(n, k)=if(n, partitions(n)[k][1], 0) \\ M. F. Hasler, Jun 06 2018

CROSSREFS

Cf. A036042, A036043, A000041 (row lengths).

Sequence in context: A052313 A271355 A211230 * A193173 A227355 A226080

Adjacent sequences:  A049082 A049083 A049084 * A049086 A049087 A049088

KEYWORD

nice,nonn,tabf,look

AUTHOR

Alford Arnold

EXTENSIONS

More terms from Wolfdieter Lang, Apr 28 2005

a(0) inserted by Franklin T. Adams-Watters, Jun 24 2014

STATUS

approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)