A390937 Number of entries in the map T after the n-th iteration, when initially T[1] = 1 is the only entry, and in subsequent iterations, T[v] := k + (T[v] if defined else 0) for each key-value pair (k, v) in the map.

1, 1, 2, 2, 3, 3, 4, 5, 7, 8, 12, 14, 17, 19, 23, 26, 29, 35, 40, 46, 50, 59, 67, 76, 86, 96, 105, 117, 127, 139, 151, 164, 177, 191, 204, 218, 230, 245, 258, 273, 287, 303, 317, 333, 347, 363, 377, 393, 407, 423, 437, 453, 467, 483, 497, 513, 527, 543, 557, 573, 587, 603, 617, 633, 647, 663

Offset

0,3

Comments

Partial sums of A390938 = number of new entries inserted at iteration n.

Links

Table of n, a(n) for n=0..65.

Formula

a(n) = Sum_{k=0..n} A390938(k).

Example

At the 8th iteration, two new entries T[16] and T[12] are inserted in addition to the five existing entries T[k = 1, 2, 4, 8 and 10]. Hence a(8) = 5 + 2 = 7.
See A390939 for more examples.

Prog

(Python)
def A390937(n):
    if not hasattr(A := A390937, 'terms'): A.terms=[1]
    while len(A.terms) <= n:
        A.terms += [A.terms[-1] + A390938(len(A.terms))]
    return A.terms[n]

Crossrefs

Cf. A390938 (first differences), A390939 (main entry for all related sequences).

Sequence in context: A367399 A113788 A018243 * A127207 A173513 A367693

Adjacent sequences: A390934 A390935 A390936 * A390938 A390939 A390940

Keyword

nonn

Author

M. F. Hasler, Nov 24 2025

Status

approved