A342611 a(0) = 0, a(1) = 1; a(2*n) = 7*a(n), a(2*n+1) = a(n) + a(n+1).

0, 1, 7, 8, 49, 15, 56, 57, 343, 64, 105, 71, 392, 113, 399, 400, 2401, 407, 448, 169, 735, 176, 497, 463, 2744, 505, 791, 512, 2793, 799, 2800, 2801, 16807, 2808, 2849, 855, 3136, 617, 1183, 904, 5145, 911, 1232, 673, 3479, 960, 3241, 3207, 19208, 3249, 3535, 1296, 5537

Offset

0,3

Links

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

Formula

G.f.: x * Product_{k>=0} (1 + 7*x^(2^k) + x^(2^(k+1))).

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], 7 a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 52}]
nmax = 52; CoefficientList[Series[x Product[(1 + 7 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, A342614, A342615.

Sequence in context: A303732 A119453 A047192 * A270009 A033044 A025630

Adjacent sequences: A342608 A342609 A342610 * A342612 A342613 A342614

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2021

Status

approved