A195821 Total number of parts that are not the smallest part in all partitions of n that do not contain 1 as a part.

0, 0, 0, 0, 1, 1, 3, 5, 7, 12, 19, 25, 37, 56, 72, 102, 138, 187, 246, 330, 422, 563, 721, 931, 1177, 1523, 1903, 2421, 3020, 3797, 4700, 5875, 7218, 8956, 10954, 13474, 16401, 20083, 24316, 29576, 35685, 43179, 51870, 62490, 74757, 89666, 106927, 127687

Offset

1,7

Comments

Total number of parts that are not the smallest part in all partitions of the head of the last section of the set of partitions of n. For more information see A195820.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = A138135(n) - A195820(n) = A138137(n) - A195820(n) - A000041(n-1).

Example

For n = 8 the seven partitions of 8 that do not contain 1 as a part are:
.   8
.   4  +  4
.  (5) +  3
.  (6) +  2
.  (3) + (3) +  2
.  (4) +  2  +  2
.   2  +  2  +  2  +  2
Note that in every partition the parts that are not the smallest part are shown between parentheses. The total number of parts that are not the smallest part is 0+0+1+1+2+1+0 = 5, so a(8) = 5.

Crossrefs

Cf. A000041, A000070, A002865, A092269, A135010, A138121, A138135, A138137, A182984, A195820.

Sequence in context: A325267 A241544 A208716 * A208772 A071810 A137576

Adjacent sequences: A195818 A195819 A195820 * A195822 A195823 A195824

Keyword

nonn

Author

Omar E. Pol, Oct 19 2011

Status

approved