A115721 - OEIS

A115721

Table of Durfee square of partitions in Abramowitz and Stegun order.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2

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OFFSET

0,10

LINKS

Table of n, a(n) for n=0..104.

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].

Eric Weisstein's World of Mathematics, Durfee Square.

FORMULA

If partition is laid out in descending order p(1),p(2),...,p(k) without repetition factors (e.g. [3,2,2,1,1,1]), a(P) = max_k min(k,p(k)).

EXAMPLE

First few rows: 0; 1,1; 1,1,1; 1,1,2,1,1; 1,1,2,1,2,1,1

CROSSREFS

Cf. A115722, A115994, A115720, A036036.

Row lengths A000041, totals A115995.

Sequence in context: A063993 A353445 A115722 * A279497 A359305 A138330

Adjacent sequences: A115718 A115719 A115720 * A115722 A115723 A115724

KEYWORD

nonn,tabf

AUTHOR

Franklin T. Adams-Watters, Mar 11 2006

STATUS

approved