A038046 Shifts left under transform T where Ta is (identity) DCONV a.

1, 1, 3, 6, 12, 17, 32, 39, 63, 81, 120, 131, 213, 226, 311, 377, 503, 520, 742, 761, 1031, 1169, 1442, 1465, 2008, 2093, 2558, 2801, 3465, 3494, 4591, 4622, 5628, 6054, 7111, 7390, 9321, 9358, 10899, 11616, 13873, 13914, 17070, 17113, 20063, 21509, 24462

Offset

1,3

Comments

Eigensequence of triangle A126988. (i.e. the sequence shifts upon multiplication from the left by triangle A126988). - Gary W. Adamson, Apr 27 2009

Number of planted achiral trees with a distinguished leaf. - Gus Wiseman, Jul 31 2018

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; a(n > 1) = Sum_{d|(n-1)} d * a((n-1)/d). - Gus Wiseman, Jul 31 2018

G.f. A(x) satisfies: A(x) = x * (1 + Sum_{j>=1} j*A(x^j)). - Ilya Gutkovskiy, May 09 2019

Example

From Gus Wiseman, Jul 31 2018: (Start)
The a(5) = 12 planted achiral trees with a distinguished leaf:
  (Oooo), (oOoo), (ooOo), (oooO),
  ((O)(o)), ((o)(O)),
  ((Ooo)), ((oOo)), ((ooO)),
  (((Oo))), (((oO))),
  ((((O)))).
(End)

Maple

a:= proc(n) option remember; `if`(n<2, n, (m-> m*
      add(a(d)/d, d=numtheory[divisors](m)))(n-1))
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 09 2019

Mathematica

a[n_]:=If[n==1, 1, Sum[d*a[(n-1)/d], {d, Divisors[n-1]}]];
Array[a, 30] (* Gus Wiseman, Jul 31 2018 *)

Crossrefs

Cf. A126988. - Gary W. Adamson, Apr 27 2009

Cf. A000081, A002033, A003238, A004111, A007554, A038046, A067824, A317580.

Sequence in context: A307042 A146952 A288570 * A345100 A162845 A239708

Adjacent sequences: A038043 A038044 A038045 * A038047 A038048 A038049

Keyword

nonn,eigen

Author

Christian G. Bower

Status

approved