A342603 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 6*a(n) + a(n+1).

0, 1, 1, 7, 1, 13, 7, 43, 1, 19, 13, 85, 7, 85, 43, 259, 1, 25, 19, 127, 13, 163, 85, 517, 7, 127, 85, 553, 43, 517, 259, 1555, 1, 31, 25, 169, 19, 241, 127, 775, 13, 241, 163, 1063, 85, 1027, 517, 3109, 7, 169, 127, 847, 85, 1063, 553, 3361, 43, 775, 517, 3361, 259, 3109, 1555, 9331, 1

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) + 6*x^(2^(k+1))).

a(2^n-1) = (6^n - 1)/5 = A003464(n); a(2^n) = 1; a(2^n+1) = 6*n + 1 = A016921(n). - Alois P. Heinz, Mar 17 2021

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 6*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 6 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 64}]
nmax = 64; CoefficientList[Series[x Product[(1 + x^(2^k) + 6 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A003464, A016921, A116528, A178243, A342633, A342634, A342635, A342636, A342637, A342638.

Sequence in context: A349173 A347965 A013600 * A060393 A060394 A203810

Adjacent sequences: A342600 A342601 A342602 * A342604 A342605 A342606

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2021

Status

approved