A390944 Value of T[4] after the n-th iteration, when the map T is initialized with T[1] = 1 and in subsequent iterations, T[v] = k + (T[v] if defined else 0) for all key-value pairs (k, v) in T; a(n) = 0 if T[4] isn't defined yet.

0, 0, 0, 0, 1, 4, 10, 12, 24, 46, 80, 160, 320, 616, 1222, 2444, 4842, 9684, 19368, 38736, 77472, 154944, 309888, 619776, 1239552, 2479104, 4958208, 9916416, 19832832, 39665664, 79331328, 158662656, 317325312, 634650624, 1269301248, 2538602496, 5077204992, 10154409984, 20308819968, 40617639936, 81235279872, 162470559744, 324941119488, 649882238976

Offset

0,6

Comments

See the main entry A390939 for additional information.

From the 8th iteration on, T[4] is the largest entry of the map T.

From the 16th iteration on, its value doubles at each iteration, cf. formula.

Links

M. F. Hasler, Table of n, a(n) for n = 0..199

Formula

a(n+1) = 2*a(n) except for n = 3, 4, 5, 6, 8, 9, 12, 13 and 15, where a(n+1) - 2*a(n) = 1, 2, 2, -8, -2, -12, -24, -10 and -46.

a(n) = 2^(n-16)*a(16) = 2^(n-15)*2421 for all n > 15.

Example

After the first few iterations, the map looks as follows:
   n | T
-----+---------------------
   0 | {1: 1}
   1 | {1: 2}
   2 | {1: 2,  2: 1}
   3 | {1: 4,  2: 2}
   4 | {1: 4,  2: 4,  4: 1}
   5 | {1: 8,  2: 4,  4: 4}        # T[4] received 1+2 from T[1] = T[2] = 4.
   6 | {1: 8,  2: 4,  4: 10, 8: 1} # T[4] received 2+4 from T[2] = T[4] = 4.
   7 | {1: 16, 2: 4,  4: 12, 8: 2, 10: 4}
   8 | {1: 16, 2: 12, 4: 24, 8: 2, 10: 4, 12: 4, 16: 1}
   9 | {1: 32, 2: 20, 4: 46, 8: 2, 10: 4, 12: 6, 16: 2, 24: 4}
The third "column" above = value in T corresponds to this sequence: Since T[4] is set only at iteration 4, we have a(0..3) = 0, then the subsequent values of T[4] are a(4, 5, ...) = 1, 4, 10, 12, 24, 46, ...

Prog

(Python)
def A390944(n):
    if not hasattr(A := A390944, 'T'): A.T = {1:1}; A.terms = [0]
    if not hasattr(A, 'N'): A.N = 17 # number of terms to compute
    while A.N > n >= len(A.terms):
        for k, v in tuple(A.T.items()): A.T[v] = A.T.get(v, 0)+k
        A.terms.append(A.T.get(4, 0))
    return A.terms[n] if n<len(A.terms) else A.terms[-1]<< n-len(A.terms)+1

Crossrefs

Cf. A390939 (main entry: list of keys as they are added to the map T).

Sequence in context: A007319 A352213 A175436 * A354024 A074939 A038464

Adjacent sequences: A390941 A390942 A390943 * A390945 A390946 A390947

Keyword

nonn,easy

Author

M. F. Hasler, Nov 24 2025

Status

approved