A355917 Variant of Inventory Sequence A342585 where indices are also counted (short version).

0, 2, 0, 4, 1, 1, 0, 6, 4, 2, 1, 2, 0, 8, 6, 5, 2, 3, 2, 2, 0, 10, 7, 9, 4, 5, 4, 3, 2, 1, 1, 1, 0, 12, 11, 11, 6, 7, 5, 5, 4, 2, 2, 2, 3, 1, 0, 14, 13, 15, 8, 9, 8, 6, 5, 5, 4, 3, 4, 2, 2, 1, 1, 0, 16, 16, 18, 10, 12, 11, 8, 6, 7, 5, 5, 6, 4, 3, 2, 2, 3, 0

Offset

1,2

Comments

See A355916 for further information.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10030

Rémy Sigrist, PARI program

Example

The first eight inventories are:
  0,
  2, 0,
  4, 1, 1, 0,
  6, 4, 2, 1, 2, 0,
  8, 6, 5, 2, 3, 2, 2, 0,
  10, 7, 9, 4, 5, 4, 3, 2, 1, 1, 1, 0,
  12, 11, 11, 6, 7, 5, 5, 4, 2, 2, 2, 3, 1, 0,
  14, 13, 15, 8, 9, 8, 6, 5, 5, 4, 3, 4, 2, 2, 1, 1, 0,
  ...

Mathematica

nn = 9; c[_] = 0; i = 1; Do[k = 0; While[c[k] > 0, Set[{a[i], a[i + 1]}, {c[k], k}]; c[a[i]]++; c[a[i + 1]]++; i += 2; k++]; Set[{a[i], a[i + 1]}, {c[k], k}]; c[a[i]]++; c[a[i + 1]]++; i += 2, nn]; Array[a[2 # - 1] &, (i - 1)/2] (* Michael De Vlieger, Sep 25 2022 *)

Prog

(PARI) See Links section.
(Python)
from collections import Counter
def aupton(terms):
    num, alst, inventory = 0, [0, 0], Counter([0, 0])
    for n in range(3, 2*terms):
        c = [inventory[num], num]
        num = 0 if c[0] == 0 else num + 1
        alst.extend(c)
        inventory.update(c)
    return alst[:2*terms:2]
print(aupton(82)) # Michael S. Branicky, Sep 25 2022

Crossrefs

Cf. A342585, A355916, A355918.

Sequence in context: A327807 A188448 A370412 * A304789 A264379 A090888

Adjacent sequences: A355914 A355915 A355916 * A355918 A355919 A355920

Keyword

nonn

Author

N. J. A. Sloane, Sep 24 2022

Extensions

More terms from Rémy Sigrist, Sep 25 2022

Status

approved