A342636 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 7*a(n) + a(n+1).

0, 1, 1, 8, 1, 15, 8, 57, 1, 22, 15, 113, 8, 113, 57, 400, 1, 29, 22, 169, 15, 218, 113, 799, 8, 169, 113, 848, 57, 799, 400, 2801, 1, 36, 29, 225, 22, 323, 169, 1198, 15, 323, 218, 1639, 113, 1590, 799, 5601, 8, 225, 169, 1296, 113, 1639, 848, 5993, 57, 1198, 799, 5993, 400, 5601, 2801

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) + 7*x^(2^(k+1))).

Maple

a:= proc(n) option remember; `if`(n<2, n, (q->
     `if`(d=1, 7*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
    end:
seq(a(n), n=0..62);  # Alois P. Heinz, Mar 17 2021

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 7 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 62}]
nmax = 62; CoefficientList[Series[x Product[(1 + x^(2^k) + 7 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342635, A342637, A342638.

Sequence in context: A173988 A349123 A158893 * A332941 A107929 A040071

Adjacent sequences: A342633 A342634 A342635 * A342637 A342638 A342639

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2021

Status

approved