%I A049982
%S A049982 0,0,1,1,2,3,3,3,6,5,5,8,6,7,12,8,8,14,9,11,17,12,11,19,14,14,22,16,14,
%T A049982 27,15,17,27,19,21,32,18,21,32,25,20,38,21,25,42,26,23,42,26,32,43,30,
%U A049982 26,49,33,33,48,33,29,59,30,35,56,37,39
%N A049982 Number of arithmetic progressions of 2 or more positive integers, strictly 
               increasing with sum n.
%H A049982 Graeme McRae, <a href="http://2000clicks.com/MathHelp/BasicSequenceA049982.htm">
               Counting arithmetic sequences whose sum is n</a>
%F A049982 a(n) has generating function x^3/(x^3-x-x^2+1) + x^6/(x^6-x^3-x^3+1) 
               + x^10/(x^10-x^6-x^4+1) + ... which is the sum k=2,3,... of x^t(k)/
               (x^t(k)-x^t(k-1)-x^k+1), where t(k) is the k-th triangular number. 
               Term k of this generating function generates the number of arithmetic 
               progressions of k positive integers, strictly increasing with sum 
               n. - Graeme McRae (g_m(AT)mcraefamily.com), Feb 08 2007
%Y A049982 Sequence in context: A126854 A115206 A093653 this_sequence A070167 A141479 
               A055081
%Y A049982 Adjacent sequences: A049979 A049980 A049981 this_sequence A049983 A049984 
               A049985
%K A049982 nonn
%O A049982 1,5
%A A049982 Clark Kimberling (ck6(AT)evansville.edu)