%I A068009
%S A068009 1,2,1,4,1,1,8,2,1,1,16,4,2,1,1,32,8,4,1,1,1,64,16,6,2,1,1,1,128,32,12,
%T A068009 4,2,1,1,1,256,64,24,8,4,2,1,1,1,512,128,44,16,8,3,1,1,1,1,1024,256,88,
%U A068009 32,14,6,3,1,1,1,1,2048,512,176,64,26,12,5,2,1,1,1,1,4096,1024,344,128
%N A068009 Square array T(m,n) with m (row) >= 1 and n (column) >= 0 read by antidiagonals: 
               number of subsets of {1,2,3,...n} that sum to 0 mod m. (Including 
               the empty set whose sum is 0).
%C A068009 When p is an odd prime, T(p,k+p) = 2*T(p,k) + (2^k * ((2^p) - 2)/p) for 
               all k >= 0 [Sophie LeBlanc]
%C A068009 When m divides n (with n >= m), T(m,n) = (1/m) Sum_{d | m and d is odd} 
               phi(d) * 2^(n/d) [N. Kitchloo and L. Pachter; D. Rusin]
%C A068009 A068009[C(i+1,2),i] = 2, A068009[C(i,2)+1,i] = A000009[i-1]+1 [AK, cf. 
               A068049]
%D A068009 N. Kitchloo and L. Pachter, An interesting result about subset sums.
%D A068009 Bill Pet, Sophie LeBlanc, Will Self et al., 2002 [See the sci.math thread 
               given above]
%H A068009 A. Karttunen, <a href="a068009s.txt">Scheme code for computing this table 
               and its rows.</a>
%H A068009 Lior Pachter, <a href="http://www.math.berkeley.edu/~lpachter/combinatorics.html">
               Subset sums</a>
%H A068009 Bill Pet, Sophie LeBlanc, Will Self et al., <a href="http://groups.google.com/
               groups?hl=en&threadm=36abe133.0201181401.410577fe%40posting.google.com&rnum=1&prev=/
               groups%3Fhl%3Den%26selm%3D36abe133.0201181401.410577fe%2540posting.google.com">
               Subsets of {1,2,3,...,n}</a> (discussion in sci.math)
%H A068009 <a href="Sindx_Su.html#subsetsums">Index entries for sequences related 
               to subset sums mod m</a>
%Y A068009 Main diagonal: A000016, super-diagonal: A063776. The first term greater 
               than one occurs on each row m in the position A002024[m] and these 
               are given in A068049.
%Y A068009 Row 1: A000079, row 2: A011782, row 3: A068010, row 5: A068011, row 6: 
               A068012, row 7: A068013, row 9: A068030, row 10: A068031, row 11: 
               A068032, row 12: A068033, row 13: A068034, row 14: A068035, row 15: 
               A068036, row 16: A068037, row 17: A068038, row 18: A068039, row 19: 
               A068040, row 20: A068041, row 21: A068042, row 25: A068043, row 32: 
               A068044, row 64: A068045.
%Y A068009 Sequence in context: A088443 A117352 A137710 this_sequence A140168 A059119 
               A127772
%Y A068009 Adjacent sequences: A068006 A068007 A068008 this_sequence A068010 A068011 
               A068012
%K A068009 nonn,nice,tabl
%O A068009 0,2
%A A068009 This entry and Scheme-code created by Antti Karttunen, Feb 11 2002