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%I
%S 0,0,1,-1,0,2,-1,1,4,8,13,7,2,-2,1,-3,0,4,9,3,8,14,7,13,6,0,-5,-1,4,
%T 10,3,9,16,24,33,23,32,42,31,41,52,64,77,63,50,38,49,37,26,16,7,15,6,
%U -2,5,-3,4,12,21,11,2,-6,1,-7,0,8,17,7,16,26,15,25,36
%N a(n)=Sum(b(i)*b(j), 1<=i<j<=n), where b(k) = A020985(k).
%C Suggested by A190173.
%H Alois P. Heinz, <a href="/A213786/b213786.txt">Table of n, a(n) for n = 0..10000</a>
%p b:= proc(n) option remember; local r;
%p `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, b(r), b(r)*(-1)^r))
%p end:
%p s:= proc(j) option remember; `if`(j<2, 0, s(j-1)+b(j-1)) end:
%p a:= proc(n) option remember; `if`(n<2, 0, a(n-1)+b(n)*s(n)) end:
%p seq (a(n), n=0..100); # _Alois P. Heinz_, Jun 23 2012
%t b[0] = 1; b[1] = 1; b[n_?EvenQ] := b[n] = b[n/2]; b[n_?OddQ] := b[n] = (-1)^((n-1)/2)*b[(n-1)/2]; a[n_] := Sum[b[i]*b[j], {i, 1, n-1}, {j, i+1, n}]; Table[a[n], {n, 0, 72}] (* _Jean-François Alcover_, Nov 27 2014 *)
%Y Cf. A020985, A190173.
%K sign
%O 0,6
%A _N. J. A. Sloane_, Jun 20 2012
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