1,4

The sequence of row lengths of this array is [1,2,3,5,7,11,15,22,30,42,56,77,...] from A000041(n), n>=1 (partition numbers).

Just for n <= 6, row n is antisymmetric due to conjugation of partitions (see links under A105806): a(n,p(n)-(k-1)) = a(n,k), k = 1,...,floor(p(n)/2). [Comment corrected by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 17 2006]

F. J. Dyson: Problems for solution nr. 4261, Am. Math. Month. 54 (1947) 418.

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].

A. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, pp. 831-2.

W. Lang: First 15 rows.

a(n, k)= rank of the k-th partition of n in Abramowitz-Stegun order (see reference). The rank of a partition is the maximal part minus the number of parts (m in the table of Abramowitz-Stegun).

[0]; [1,-1]; [2,0,-2]; [3,1,0,-1,-3]; [4,2,1,0,-1,-2,-4]; [5,3,2,1,1,0,-1,-1,-2,-3,-5]; ...

Row 3 for partitions of 3 in the mentioned order: 3,(1,2),1^3 with ranks 2,0,-2.

Adjacent sequences: A105802 A105803 A105804 this_sequence A105806 A105807 A105808

Sequence in context: A160706 A087509 A089596 this_sequence A049581 A114327 A073450

sign,easy,tabf

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 28 2005