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A340248 Sum of the second largest parts s of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t. 3
0, 0, 0, 1, 1, 2, 4, 7, 10, 15, 22, 29, 42, 51, 71, 87, 116, 132, 177, 201, 259, 289, 368, 404, 508, 550, 681, 738, 900, 959, 1164, 1239, 1482, 1569, 1863, 1962, 2313, 2424, 2835, 2971, 3448, 3590, 4150, 4318, 4954, 5142, 5872, 6080, 6912, 7140, 8078, 8343, 9395, 9672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..54.

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))) * i.

MATHEMATICA

Table[Sum[Sum[Sum[i*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, A340246, A340247, A340249.

Sequence in context: A049640 A179385 A024668 * A188951 A226136 A176099

Adjacent sequences: A340245 A340246 A340247 * A340249 A340250 A340251

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jan 01 2021

STATUS

approved

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Last modified February 5 09:20 EST 2023. Contains 360082 sequences. (Running on oeis4.)