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%I #7 Jun 19 2023 08:04:31
%S 1,1,3,4,8,12,18,27,40,58,83,118,195,242,-1387,-338,75876,44491,
%T -3099115,-2028539,129829195,91749709,-5687984421,-4236497556,
%U 263653557716,204087552038,-12979768392096,-10348229609729,679042377362009,554161706136054,-37712174126966326
%N a(n) = Sum_{k=0..floor(n/2)} binomial(n - k*(k-1)/2, k).
%t Table[ Sum[ Binomial[ n - i*(i - 1)/2, i ], {i, 0, Floor[ n/2 ] } ], {n, 0, 30} ]
%o (PARI) a(n) = sum(k=0, n\2, binomial(n - k*(k-1)/2, k)); \\ _Michel Marcus_, Jun 19 2023
%Y Cf. A063978.
%K sign
%O 0,3
%A Helmut Schnitzspan (HSchnitzspan(AT)gmx.de), Sep 05 2001
%E More terms from _Robert G. Wilson v_, Sep 06 2001
%E Missing a(0)=1 inserted by _Sean A. Irvine_, Jun 18 2023