A342614 a(0) = 0, a(1) = 1; a(2*n) = 8*a(n), a(2*n+1) = a(n) + a(n+1).

0, 1, 8, 9, 64, 17, 72, 73, 512, 81, 136, 89, 576, 145, 584, 585, 4096, 593, 648, 217, 1088, 225, 712, 665, 4608, 721, 1160, 729, 4672, 1169, 4680, 4681, 32768, 4689, 4744, 1241, 5184, 865, 1736, 1305, 8704, 1313, 1800, 937, 5696, 1377, 5320, 5273, 36864, 5329, 5768, 1881, 9280

Offset

0,3

Links

Table of n, a(n) for n=0..52.

Formula

G.f.: x * Product_{k>=0} (1 + 8*x^(2^k) + x^(2^(k+1))).

Mathematica

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}]
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]

Crossrefs

Cf. A002487, A178569, A178590, A237711, A244643, A342610, A342611, A342615.

Sequence in context: A121330 A152189 A042873 * A033045 A025633 A249697

Adjacent sequences: A342611 A342612 A342613 * A342615 A342616 A342617

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2021

Status

approved