A343320 Number of partitions of n into 4 parts s,t,u,v such that (s+t+u+v) | s*t*u*v.

0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 6, 0, 2, 5, 11, 0, 13, 0, 19, 12, 6, 0, 43, 15, 9, 24, 40, 0, 52, 0, 55, 30, 16, 45, 136, 0, 20, 44, 141, 0, 110, 0, 105, 160, 30, 0, 258, 69, 141, 75, 149, 0, 216, 124, 298, 96, 49, 0, 509, 0, 56, 346, 362, 176, 295, 0, 260, 140

Offset

1,8

Links

Table of n, a(n) for n=1..69.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (1 - ceiling(i*j*k*(n-i-j-k)/n) + floor(i*j*k*(n-i-j-k)/n)).

Example

a(8) = 2; [1,1,2,4] and [2,2,2,2], where (1+1+2+4) | 1*1*2*4 and (2+2+2+2) | 2*2*2*2.
a(9) = 1; [1,2,3,3], where (1+2+3+3) | 1*2*3*3.

Mathematica

Table[Sum[Sum[Sum[(1 - Ceiling[i*j*k*(n - i - j - k)/n] + Floor[i*j*k*(n - i - j - k)/n]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Crossrefs

Cf. A343270.

Sequence in context: A229892 A064879 A173591 * A156603 A156612 A351791

Adjacent sequences: A343317 A343318 A343319 * A343321 A343322 A343323

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 11 2021

Status

approved