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A220479 Total number of smallest parts that are also emergent parts in all partitions of n. 5
0, 0, 0, 1, 0, 3, 1, 5, 5, 10, 8, 22, 19, 33, 40, 62, 67, 107, 118, 175, 208, 282, 331, 462, 542, 712, 859, 1112, 1323, 1709, 2030, 2568, 3078, 3830, 4577, 5687, 6760, 8291, 9885, 12045, 14290, 17334, 20515, 24710, 29242, 35004, 41282, 49283, 57963, 68836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

For the definition of emergent parts see A182699.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A092269(n) - A000070(n-1) - A002865(n) = A092269(n) - A120452(n+1) = A195820(n) - A002865(n).

a(n) = A092269(n) - A000041(n) - A000070(n-2), n >= 2.

a(n) = A215513(n) - A000070(n-2), n >= 2.

a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*sqrt(3)*n). - Vaclav Kotesovec, Jul 31 2017

CROSSREFS

Cf. A000041, A000070, A002865, A006128, A092269, A120452, A182699, A182709, A195820, A206437, A215513.

Sequence in context: A124741 A213952 A205873 * A146913 A146252 A181641

Adjacent sequences:  A220476 A220477 A220478 * A220480 A220481 A220482

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jan 12 2013

EXTENSIONS

a(43) corrected by Vaclav Kotesovec, Jul 31 2017

STATUS

approved

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Last modified May 30 15:21 EDT 2020. Contains 334726 sequences. (Running on oeis4.)