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

Author

Omar E. Pol, Oct 19 2011

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Formula

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