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A308991 Sum of the seventh largest parts in the partitions of n into 8 parts. 8
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 32, 45, 60, 82, 107, 143, 184, 240, 303, 387, 484, 609, 753, 934, 1142, 1401, 1695, 2056, 2468, 2967, 3532, 4208, 4974, 5882, 6904, 8105, 9458, 11033, 12798, 14840, 17124, 19750, 22674, 26018, 29735 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..51.

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)} o.

a(n) = A308989(n) - A308990(n) - A308992(n) - A308994(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o, {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, A308992, A308994, A308995, A308996, A308997, A308998.

Sequence in context: A232482 A253062 A117590 * A326467 A326592 A226541

Adjacent sequences:  A308988 A308989 A308990 * A308992 A308993 A308994

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 04 2019

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)