A350677 a(n) is the sum of the numbers k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).

0, 0, 1, 1, 6, 1, 11, 1, 22, 13, 18, 1, 39, 11, 29, 1, 88, 5, 70, 1, 82, 1, 84, 1, 158, 23, 124, 1, 134, 1, 163, 1, 428, 151, 272, 73, 328, 117, 315, 87, 452, 185, 307, 97, 258, 109, 228, 35, 444, 171, 331, 77, 378, 81, 265, 37, 345, 135, 251, 41, 238, 45, 194

Offset

0,5

Comments

The definition is recursive: a(n) depends on prior terms (a(0), ..., a(n-1)); a(0) = a(1) = 0 correspond to empty sums.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  --------------------------
   0     0  {}
   1     0  {0}
   2     1  {0, 1}
   3     1  {0, 1}
   4     6  {0, 1, 2, 3}
   5     1  {0, 1}
   6    11  {0, 1, 2, 3, 5}
   7     1  {0, 1}
   8    22  {0, 1, 2, 3, 4, 5, 7}
   9    13  {0, 1, 4, 8}
  10    18  {0, 1, 2, 3, 5, 7}
  11     1  {0, 1}
  12    39  {0, 1, 2, 3, 5, 7, 10, 11}

Maple

a:= proc(n) option remember; add(
     `if`(Bits[And](n, a(j))=0, j, 0), j=0..n-1)
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Feb 28 2022

Prog

(PARI) for (n=1, #a=vector(63), print1 (a[n]=sum(k=1, n-1, if (bitand(a[k], n-1)==0, k-1, 0))", "))

Crossrefs

Cf. A350802, A351886.

Sequence in context: A259671 A224524 A348982 * A046618 A328898 A216605

Adjacent sequences: A350674 A350675 A350676 * A350678 A350679 A350680

Keyword

base,nonn

Author

Rémy Sigrist, Feb 25 2022

Status

approved