A348540 Number of partitions of n into 3 parts whose smallest part divides the largest part.

0, 0, 1, 1, 2, 3, 3, 4, 6, 6, 6, 9, 9, 10, 12, 12, 13, 16, 15, 18, 20, 19, 19, 24, 25, 25, 27, 28, 28, 33, 31, 34, 37, 36, 38, 42, 41, 42, 44, 47, 47, 52, 50, 53, 57, 54, 54, 61, 62, 64, 65, 66, 66, 71, 71, 74, 76, 75, 75, 84, 82, 83, 87, 87, 90, 93, 91, 94, 96, 99, 97, 106

Offset

1,5

Links

Table of n, a(n) for n=1..72.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling((n-i-j)/j) + floor((n-i-j)/j)).

Mathematica

a[n_] := Sum[1 - Ceiling[(n - i - j)/j] + Floor[(n - i - j)/j], {j, 1, Floor[n/3]}, {i, j, Floor[(n - j)/2]}]; Array[a, 100] (* Amiram Eldar, Oct 22 2021 *)

Crossrefs

Sequence in context: A290585 A106464 A093003 * A118096 A296440 A181692

Adjacent sequences: A348537 A348538 A348539 * A348541 A348542 A348543

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 21 2021

Status

approved