A342635 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 5*a(n) + a(n+1).

0, 1, 1, 6, 1, 11, 6, 31, 1, 16, 11, 61, 6, 61, 31, 156, 1, 21, 16, 91, 11, 116, 61, 311, 6, 91, 61, 336, 31, 311, 156, 781, 1, 26, 21, 121, 16, 171, 91, 466, 11, 171, 116, 641, 61, 616, 311, 1561, 6, 121, 91, 516, 61, 641, 336, 1711, 31, 466, 311, 1711, 156, 1561, 781, 3906, 1, 31, 26

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) + 5*x^(2^(k+1))).

a(n) == 1 (mod 5) for n >= 1. - Hugo Pfoertner, Mar 17 2021

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 5*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..66);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 5 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 66}]
nmax = 66; CoefficientList[Series[x Product[(1 + x^(2^k) + 5 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342636, A342637, A342638.

Sequence in context: A046618 A328898 A216605 * A107348 A342917 A040041

Adjacent sequences: A342632 A342633 A342634 * A342636 A342637 A342638

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2021

Status

approved