A369917 Number of partitions of n into two distinct arithmetic numbers.

0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 3, 2, 4, 2, 5, 3, 4, 3, 5, 4, 5, 4, 6, 3, 5, 3, 6, 5, 8, 5, 9, 5, 7, 4, 8, 6, 9, 7, 11, 7, 9, 7, 11, 9, 13, 8, 14, 8, 11, 8, 13, 11, 14, 11, 16, 12, 15, 11, 15, 12, 16, 13, 18, 12, 15, 14, 18, 16, 19, 15, 20, 14, 16, 15

Offset

1,8

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

Example

a(14) = 2 ways (13+1 = 11+3, we do not count 7+7).

Mathematica

a[n_] := Boole[IntegerQ[Mean[Divisors[n]]]]; Table[Sum[a[k]*a[n - k], {k, Floor[(n - 1)/2]}], {n, 100}]

Crossrefs

Cf. A003601, A245656, A369916.

Sequence in context: A064693 A325614 A361746 * A319608 A230850 A072085

Adjacent sequences: A369914 A369915 A369916 * A369918 A369919 A369920

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Feb 05 2024

Status

approved