A342637 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 8*a(n) + a(n+1).

0, 1, 1, 9, 1, 17, 9, 73, 1, 25, 17, 145, 9, 145, 73, 585, 1, 33, 25, 217, 17, 281, 145, 1169, 9, 217, 145, 1233, 73, 1169, 585, 4681, 1, 41, 33, 289, 25, 417, 217, 1753, 17, 417, 281, 2393, 145, 2329, 1169, 9361, 9, 289, 217, 1881, 145, 2393, 1233, 9937, 73, 1753, 1169, 9937, 585

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..16384

Formula

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

a(n) == 1 (mod 8) for n >= 1. - Hugo Pfoertner, Mar 17 2021

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 8*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 8 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 60}]
nmax = 60; CoefficientList[Series[x Product[(1 + x^(2^k) + 8 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342635, A342636, A342638.

Sequence in context: A349143 A014721 A054018 * A010170 A317051 A013616

Adjacent sequences: A342634 A342635 A342636 * A342638 A342639 A342640

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2021

Status

approved