A369916 Number of partitions of n into two arithmetic numbers.

0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 1, 3, 1, 3, 1, 3, 2, 4, 2, 5, 3, 5, 3, 5, 4, 6, 4, 7, 3, 6, 3, 6, 5, 9, 5, 9, 5, 8, 4, 9, 6, 10, 7, 12, 7, 10, 7, 11, 9, 13, 8, 14, 8, 12, 8, 13, 11, 15, 11, 17, 12, 16, 11, 15, 12, 17, 13, 18, 12, 16, 14, 18, 16, 20, 15, 21, 14, 17, 15

Offset

1,6

Links

Table of n, a(n) for n=1..79.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k), where c = A245656.

Example

a(14) = 3 ways (13+1 = 11+3 = 7+7).

Mathematica

a[n_] := Boole[IntegerQ[Mean[Divisors[n]]]]; Table[Sum[a[k]*a[n - k], {k, Floor[n/2]}], {n, 100}]

Crossrefs

Cf. A003601, A245656, A369917 (distinct).

Sequence in context: A175494 A055399 A029426 * A085342 A025825 A293224

Adjacent sequences: A369913 A369914 A369915 * A369917 A369918 A369919

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved