A342638 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 9*a(n) + a(n+1).

0, 1, 1, 10, 1, 19, 10, 91, 1, 28, 19, 181, 10, 181, 91, 820, 1, 37, 28, 271, 19, 352, 181, 1639, 10, 271, 181, 1720, 91, 1639, 820, 7381, 1, 46, 37, 361, 28, 523, 271, 2458, 19, 523, 352, 3349, 181, 3268, 1639, 14761, 10, 361, 271, 2620, 181, 3349, 1720, 15571, 91, 2458, 1639, 15571, 820

Offset: 0

Author

Ilya Gutkovskiy, Mar 17 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342635, A342636, A342637.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 9*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], 9 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 60}]
nmax = 60; CoefficientList[Series[x Product[(1 + x^(2^k) + 9 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Formula

G.f.: x * Product_{k>=0} (1 + x^(2^k) + 9*x^(2^(k+1))).