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A308996 Sum of the third largest parts in the partitions of n into 8 parts. 8
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 63, 92, 128, 183, 246, 337, 448, 597, 774, 1012, 1291, 1656, 2085, 2627, 3264, 4064, 4987, 6127, 7450, 9055, 10901, 13126, 15669, 18701, 22157, 26228, 30858, 36279, 42397, 49509, 57527, 66773, 77148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..49.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} j.

a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308997(n) - A308998(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[j, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]

CROSSREFS

Cf. A026814, A308989, A308990, A308991, A308992, A308994, A308995, A308997, A308998.

Sequence in context: A308871 A325546 A308931 * A326471 A326596 A170804

Adjacent sequences:  A308993 A308994 A308995 * A308997 A308998 A308999

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 04 2019

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)