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%I #72 Jan 05 2023 21:19:27
%S 1,3,7,10,18,25,30,36,52,67,80,94,103,113,125,136,168,199,228,258,283,
%T 309,337,364,381,399,419,438,462,485,506,528,592,655,716,778,835,893,
%U 953,1012,1061,1111,1163,1214,1270,1325,1378,1432,1465,1499,1535,1570
%N Partial sums of A066194.
%C n^2/2 + n/2 <= a(n) <= (31/50)*n^2 + n/2. The lower and upper bounds are attained at n=2^k and n=5*2^k for k >= 0.
%H Alois P. Heinz, <a href="/A342448/b342448.txt">Table of n, a(n) for n = 1..16384</a>
%F a(n) = A268836(n)/2 + n. - _Kevin Ryde_, Mar 12 2021
%F a(1) = 1; a(n) = [n == 0 (mod 2)]*(4*a(n/2) - n/2) + [n == 1 (mod 2)]*(2*a((n - 1)/2)+2*a((n + 1)/2)-(n-1)/2 - A010060(n)) where [] is an Iverson bracket
%p b:= proc(n) option remember; `if`(n<2, n,
%p Bits[Xor](n, b(iquo(n, 2))))
%p end:
%p a:= proc(n) a(n):= 1+`if`(n<2, 0, a(n-1)+b(n-1)) end:
%p seq(a(n), n=1..60); # _Alois P. Heinz_, Mar 14 2021
%t a[1]=1;
%t a[n_/;EvenQ[n]]:= a[n] = 4a[n/2] - n/2;
%t a[n_/;OddQ[n]]:= a[n] = 2a[(n - 1)/2]+2a[(n + 1)/2]-(n-1)/2 - ThueMorse[n];
%t (* Second program: *)
%t b[n_] := If[n==0, 0, BitXor@@Table[Floor[n/2^m], {m, 0, Floor[Log[2, n]]}]];
%t A066194 = Table[b[n]+1, {n, 0, 60}];
%t A066194 // Accumulate (* _Jean-François Alcover_, Sep 10 2022 *)
%Y Cf. A066194, A268836, A007814, A000120, A010060, A000035.
%K nonn,look
%O 1,2
%A _John Erickson_, Mar 12 2021
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