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A096771 Triangle read by rows: T(n,m) counts partitions of n that (just) fit inside an m X m box, but not in an (m-1) X (m-1) box. Partitions of n with Max(max part, length)= m. 15
1, 0, 2, 0, 1, 2, 0, 1, 2, 2, 0, 0, 3, 2, 2, 0, 0, 3, 4, 2, 2, 0, 0, 2, 5, 4, 2, 2, 0, 0, 1, 7, 6, 4, 2, 2, 0, 0, 1, 6, 9, 6, 4, 2, 2, 0, 0, 0, 7, 11, 10, 6, 4, 2, 2, 0, 0, 0, 5, 14, 13, 10, 6, 4, 2, 2, 0, 0, 0, 5, 15, 19, 14, 10, 6, 4, 2, 2, 0, 0, 0, 3, 17, 22, 21, 14, 10, 6, 4, 2, 2, 0, 0, 0, 2, 17, 29 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums are A000041. Columns are finite and sum to A051924. The Floor(n/2) terms are the reverse of 2* A000041.

LINKS

Table of n, a(n) for n=1..97.

Findstat, FindStat - St000784: The maximum of the length and the largest part of the integer partition

EXAMPLE

T(5,3)=3, counting 32, 311 and 221.

From Gus Wiseman, Apr 12 2019: (Start)

Triangle begins:

  1

  0  2

  0  1  2

  0  1  2  2

  0  0  3  2  2

  0  0  3  4  2  2

  0  0  2  5  4  2  2

  0  0  1  7  6  4  2  2

  0  0  1  6  9  6  4  2  2

  0  0  0  7 11 10  6  4  2  2

  0  0  0  5 14 13 10  6  4  2  2

  0  0  0  5 15 19 14 10  6  4  2  2

  0  0  0  3 17 22 21 14 10  6  4  2  2

  0  0  0  2 17 29 27 22 14 10  6  4  2  2

  0  0  0  1 17 33 36 29 22 14 10  6  4  2  2

  0  0  0  1 15 39 45 41 30 22 14 10  6  4  2  2

  0  0  0  0 14 41 57 52 43 30 22 14 10  6  4  2  2

  0  0  0  0 11 47 67 69 57 44 30 22 14 10  6  4  2  2

  0  0  0  0  9 46 81 85 76 59 44 30 22 14 10  6  4  2  2

(End)

MATHEMATICA

Table[Count[Partitions[n], q_List /; Max[Length[q], Max[q]]===k], {n, 16}, {k, n}]

CROSSREFS

Cf. A051924, A096272, A096597, A115994, A252464, A263297, A325193.

Related triangles are A115720, A325188, A325189, A325192, A325200, with Heinz-encoded versions A257990, A325169, A065770, A325178, A325195.

Sequence in context: A215590 A097203 A025850 * A129714 A022333 A055087

Adjacent sequences:  A096768 A096769 A096770 * A096772 A096773 A096774

KEYWORD

easy,nonn,tabl

AUTHOR

Wouter Meeussen, Aug 21 2004

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)