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%I #17 Dec 26 2022 13:10:03
%S 0,0,0,1,-1,0,4,7,-7,-6,0,3,13,18,28,35,-35,-34,-24,-21,-5,0,14,21,43,
%T 52,70,81,105,118,140,155,-155,-154,-136,-133,-105,-100,-78,-71,-35,
%U -26,0,11,47,60,90,105,151,168,202,221,265,286,324,347,399,424,466,493,545,574,620,651,-651,-650,-616,-613,-561
%N a(n) = A000217(n) - A048702(n).
%C The positions of the zeros seem to be given by A000975.
%H G. C. Greubel, <a href="/A075113/b075113.txt">Table of n, a(n) for n = 0..1000</a>
%F a(A000225(n)) = ((2^n)-1)*(2^(n-1)) - (2^(2n) - 1)/3 = A006095(n).
%t A048702 := Join[{0}, Reap[For[k = 1, k < 1500, k += 2, bb = IntegerDigits[k, 2]; If[bb == Reverse[bb], If[EvenQ[Length[bb]], Sow[k/3]]]]][[2, 1]]]; Table[n*(n + 1)/2 - A048702[[n + 1]], {n, 0, 50}] (* _G. C. Greubel_, Sep 26 2017 *)
%o (PARI) a01(n) = my(f); f = length(binary(n)) - 1; 2^(f+1)*n + sum(i=0, f, bittest(n, i) * 2^(f-i)); \\ A048701
%o a(n) = n*(n+1)/2 - a01(n)/3; \\ A006095
%o (Python)
%o def A075113(n: int) -> int:
%o s = bin(n)[2:]
%o return n * (n + 1) // 2 - int(s + s[::-1], 2) // 3
%o print([A075113(n) for n in range(69)]) # _Peter Luschny_, Dec 14 2022
%Y Cf. A000217, A048701, A048702.
%Y Cf. A000975, A000225, A006095.
%K sign
%O 0,7
%A _Antti Karttunen_, Sep 02 2002
%E Definition corrected by _Georg Fischer_, Dec 13 2022
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