%I A069999
%S A069999 1,2,3,5,7,9,13,18,21,27,34,39,46,54,61,72,83,92,106,118,130,145,162,
%T A069999 176,193,209,226,246,265,284,308,330,352,375,402,426,453,480,508,538,
%U A069999 570,598,631,661,694,730,765,800,835,872,911,951,992,1030,1071,1115
%N A069999 Number of possible dimensions for commutators of n X n matrices; it is 
               independent of the field. Or, given a partition P = (p_1, p_2, ..., 
               p_m) of n with p_1 >= p_2 >= ... >= p_m, let S(P) = sum_j (2j-1)p_j; 
               then a(n) = number of integers that are an S(P) for some partition.
%C A069999 Or, given such a partition P of n, let T(P) = sum_i p_i^2; then a(n) 
               = number of integers that are a T(P) for some P. While T(P) need 
               not equal S(P) for a given partition, the two sets of integers are 
               equal. Or, expand the infinite product prod_k 1/(1-x^{k^2}y^k) as 
               a power series; then a(n) = number of terms of the form x^my^n having 
               a nonzero coefficient.
%D A069999 Zachary Albertson and Evan Willett, "Possible Dimensions of Commutators 
               of Matrices", Senior Thesis, Wake Forest University, May 09, 2002.
%H A069999 David Savitt and R. P. Stanley, A Note on the Symmetric Powers of the 
               Standard Representation of S_n, <a href="http://www.combinatorics.org/
               ">Electronic J. Combinat.</a>, 7 (2000) #R6.
%F A069999 No generating function is known.
%Y A069999 Sequence in context: A032459 A028870 A057886 this_sequence A035563 A028378 
               A143587
%Y A069999 Adjacent sequences: A069996 A069997 A069998 this_sequence A070000 A070001 
               A070002
%K A069999 easy,nonn,nice
%O A069999 1,2
%A A069999 Jim Kuzmanovich (kuz(AT)wfu.edu), Apr 26 2002
%E A069999 More terms from Robert Gerbicz (gerbicz(AT)freemail.hu), Aug 27 2002