A091948 Number of values of k, 0 <= k <= n, satisfying A002487(k) = A002487(n).

1, 1, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 4, 2, 5, 3, 3, 1, 5, 1, 4, 2, 4, 3, 5, 2, 6, 4, 4, 6, 6, 1, 7, 1, 5, 1, 5, 1, 7, 2, 3, 1, 8, 1, 6, 2, 5, 3, 7, 2, 9, 2, 4, 3, 8, 2, 8, 4, 6, 4, 10, 2, 7, 9, 3, 5, 11, 1, 5, 3, 7, 1, 6, 1, 10, 1, 3, 4, 9, 2, 7, 1, 5, 1, 5, 2, 12, 2, 3, 2, 11, 1, 6, 8, 6, 9, 7, 2, 12, 3, 4

Offset: 0

Author

Benoit Cloitre, Mar 11 2004

Keywords

• nonn
• look

Comments

This sequence is the ordinal transform of A002487. - Rémy Sigrist, Dec 28 2022

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, PARI program
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A091945.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, n,
      (q-> b(q)+(n-2*q)*b(n-q))(iquo(n, 2)))
    end:
p:= proc() 0 end:
a:= proc(n) option remember; local t;
      t:= b(n); p(t):= p(t)+1
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 31 2022

Mathematica

b[n_] := b[n] = If[n < 2, n,
   Function[q, b[q] + (n - 2*q)*b[n - q]][Quotient[n, 2]]];
p[_] = 0;
a[n_] := a[n] = With[{t = b[n]}, p[t] = p[t]+1];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 20 2024, after Alois P. Heinz *)

PARI

\\ See Links section.

Formula

a(n) = 1 iff n belongs to A091945. - Rémy Sigrist, Dec 28 2022

Extensions

a(0) = 1 prepended and name adapted by Rémy Sigrist, Dec 28 2022