A342633 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 3*a(n) + a(n+1).

0, 1, 1, 4, 1, 7, 4, 13, 1, 10, 7, 25, 4, 25, 13, 40, 1, 13, 10, 37, 7, 46, 25, 79, 4, 37, 25, 88, 13, 79, 40, 121, 1, 16, 13, 49, 10, 67, 37, 118, 7, 67, 46, 163, 25, 154, 79, 241, 4, 49, 37, 136, 25, 163, 88, 277, 13, 118, 79, 277, 40, 241, 121, 364, 1, 19, 16, 61, 13, 88, 49, 157

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) + 3*x^(2^(k+1))).

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 3*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..71);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 3 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 71}]
nmax = 71; CoefficientList[Series[x Product[(1 + x^(2^k) + 3 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A116528, A178243, A342603, A342634, A342635, A342636, A342637, A342638.

Sequence in context: A262606 A286387 A363974 * A094649 A344970 A135857

Adjacent sequences: A342630 A342631 A342632 * A342634 A342635 A342636

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2021

Status

approved