%I A035313
%S A035313 1,3,9,26,66,154,346,771,1726,3887,8768,19700,43890,96717,210665,453893,
%T A035313 968903,2053260,4328489,9093971,19068611,39943689,83628399,175018523,
%U A035313 366081209,765102907,1597315656,3330380593,6933810145
%N A035313 (Largest) diagonal of the Zorach additive triangle.
%C A035313 Comment from Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Apr 22 
               2007: (Start)
%C A035313 Starting with 1, smallest sequence for which:
%C A035313 all its terms a1(n).............................. 1,3,9,26,66
%C A035313 all terms of first differences a2(n)=a1(n+1)-a1(n) 2,6,17,40
%C A035313 all terms of second differences a3(n)=a2(n+1)-a2(n) 4,11,23
%C A035313 ...
%C A035313 all terms of (1+i)th differences ai(n)=ai-1(n+1)-ai-1(n)
%C A035313 are different for any n and any i (End)
%H A035313 A. C. Zorach, <a href="http://www.cazort.net/static/triangle.php">Additive 
               triangle</a>
%e A035313 Start with 1; 2 is the next, then add 1+2 to get 3, then 4 is next, then 
               4+2=6 and 6+3 is 9, then 5 is not next because 5+4=9 and 9 was already 
               used, so 7 is next...which ultimately generates 26 in the final column...
%Y A035313 Cf. A035311, A035312, A035358.
%Y A035313 Sequence in context: A119851 A119825 A037260 this_sequence A055293 A034531 
               A048470
%Y A035313 Adjacent sequences: A035310 A035311 A035312 this_sequence A035314 A035315 
               A035316
%K A035313 nonn,easy,nice
%O A035313 0,2
%A A035313 Alexander C. Zorach (cazort(AT)udel.edu)
%E A035313 More terms from Christian G. Bower (bowerc(AT)usa.net) and Dean Hickerson 
               dean.hickerson(AT)yahoo.com