A348535 Sum of all the parts in the partitions of n into 3 parts that divide the product of the other two parts within each partition.

0, 0, 3, 2, 7, 9, 16, 18, 30, 28, 49, 44, 71, 69, 93, 96, 135, 124, 177, 146, 195, 205, 279, 242, 297, 312, 362, 332, 469, 383, 539, 492, 557, 594, 627, 570, 794, 761, 834, 758, 1022, 836, 1137, 984, 1066, 1171, 1412, 1188, 1409, 1330, 1499, 1454, 1839, 1555, 1749, 1622

Offset

1,3

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to partitions

Formula

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

Example

a(9) = 30; The partitions of 9 into 3 parts are (1,1,7), (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4) and (3,3,3). The sums of the parts that divide the product of the other two, within each partition in the list above are, respectively: (1+1) + (1+2) + (1) + (1+4+4) + (2+2) + (2) + (3+3+3) which equals 30.

Mathematica

Block[{c}, c[n_] := 1 - Ceiling[n] + Floor[n]; Array[Sum[Sum[j*c[i*(# - i - j)/j] + i*c[j*(# - i - j)/i] + (# - i - j)*c[i*j/(# - i - j)], {i, j, Floor[(# - j)/2]}], {j, Floor[#/3]}] &, 56] ] (* Michael De Vlieger, Oct 21 2021 *)

Crossrefs

Cf. A348531.

Sequence in context: A351904 A351903 A359973 * A018891 A034423 A193859

Adjacent sequences: A348532 A348533 A348534 * A348536 A348537 A348538

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 21 2021

Status

approved