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%I #5 Mar 17 2021 07:58:09
%S 0,1,8,9,64,17,72,73,512,81,136,89,576,145,584,585,4096,593,648,217,
%T 1088,225,712,665,4608,721,1160,729,4672,1169,4680,4681,32768,4689,
%U 4744,1241,5184,865,1736,1305,8704,1313,1800,937,5696,1377,5320,5273,36864,5329,5768,1881,9280
%N a(0) = 0, a(1) = 1; a(2*n) = 8*a(n), a(2*n+1) = a(n) + a(n+1).
%F G.f.: x * Product_{k>=0} (1 + 8*x^(2^k) + x^(2^(k+1))).
%t a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], 8 a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 52}]
%t nmax = 52; CoefficientList[Series[x Product[(1 + 8 x^(2^k) + x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%Y Cf. A002487, A178569, A178590, A237711, A244643, A342610, A342611, A342615.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 16 2021
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