A340246 Sum of the smallest parts q of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

0, 0, 0, 1, 1, 1, 2, 4, 5, 7, 10, 13, 17, 21, 28, 35, 44, 50, 64, 75, 92, 104, 128, 143, 172, 190, 228, 252, 297, 321, 378, 411, 477, 513, 594, 636, 729, 777, 888, 946, 1072, 1132, 1280, 1354, 1520, 1600, 1792, 1882, 2096, 2196, 2440, 2555, 2825, 2945, 3250, 3390, 3725, 3875

Offset

1,7

Links

Table of n, a(n) for n=1..58.

Formula

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

Mathematica

Table[Sum[Sum[Sum[k*Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]

Crossrefs

Cf. A062890, A340247, A340248, A340249.

Sequence in context: A279022 A226807 A211523 * A062463 A056716 A223729

Adjacent sequences: A340243 A340244 A340245 * A340247 A340248 A340249

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 01 2021

Status

approved