A342634 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 4*a(n) + a(n+1).

0, 1, 1, 5, 1, 9, 5, 21, 1, 13, 9, 41, 5, 41, 21, 85, 1, 17, 13, 61, 9, 77, 41, 169, 5, 61, 41, 185, 21, 169, 85, 341, 1, 21, 17, 81, 13, 113, 61, 253, 9, 113, 77, 349, 41, 333, 169, 681, 5, 81, 61, 285, 41, 349, 185, 761, 21, 253, 169, 761, 85, 681, 341, 1365, 1, 25, 21, 101, 17

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, A342635, A342636, A342637, A342638.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 4*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..68);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 4 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 68}]
nmax = 68; CoefficientList[Series[x Product[(1 + x^(2^k) + 4 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) + 4*x^(2^(k+1))).

a(n) == 1 (mod 4) for n >= 1. - Hugo Pfoertner, Mar 17 2021