A348537 Number of partitions of n into 3 parts whose largest part divides n.

0, 0, 1, 1, 0, 2, 0, 2, 1, 2, 0, 4, 0, 3, 1, 4, 0, 5, 0, 5, 1, 5, 0, 7, 0, 6, 1, 7, 0, 8, 0, 8, 1, 8, 0, 10, 0, 9, 1, 10, 0, 11, 0, 11, 1, 11, 0, 13, 0, 12, 1, 13, 0, 14, 0, 14, 1, 14, 0, 16, 0, 15, 1, 16, 0, 17, 0, 17, 1, 17, 0, 19, 0, 18, 1, 19, 0, 20, 0, 20, 1, 20, 0, 22, 0

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10480

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/(n-i-j)) + floor(n/(n-i-j))).

Mathematica

Array[Sum[Sum[(1 - Ceiling[#/(# - i - j)] + Floor[#/(# - i - j)]), {i, j, Floor[(# - j)/2]} ], {j, Floor[#/3]} ] &, 85] (* Michael De Vlieger, Oct 21 2021 *)

Prog

(PARI) A348537(n) = sum(j=1, (n\3), sum(i=j, ((n-j)\2), (1 - ceil(n/(n-i-j)) + floor(n/(n-i-j))))); \\ Antti Karttunen, Feb 18 2023

Crossrefs

Cf. A069905.

Sequence in context: A307409 A070824 A174725 * A071459 A319164 A070288

Adjacent sequences: A348534 A348535 A348536 * A348538 A348539 A348540

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 21 2021

Status

approved