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%I #5 Mar 30 2012 18:37:43
%S 1,4,18,72,324,1360,6280,27296,128784,573760,2752032,12485248,
%T 60652608,278988032,1368979584,6365514240,31488733440,147697177600,
%U 735486927360,3474529986560,17398140748800,82683153633280,415966710171648
%N Sum of absolute values of list generated by n replacements of k by {-1-|k|, .., 1+|k|} with increment 2, starting with {1}.
%C Sum of absolute values of list elements starting from 0, (A083691), gives twice A083693, but with an initial zero.
%F A083691(n+2)/2-A083691(n+1)
%e 0, 1 and 2 substitutions produce lengths 1, 3 and 10:
%e {1}; {-2,0,2}; {-3,-1,1,3, -1,1, -3,-1,1,3} with sums of absolute values 1,4,18.
%t Table[Plus@@Abs@Flatten[Nest[ #/.k_Integer:>Table[i, {i, -1-Abs[k], Abs[k]+1, 2}]&, {1}, w]], {w, 0, 10}]
%Y Cf. A083691, A083692.
%K nonn
%O 0,2
%A _Wouter Meeussen_, May 03 2003