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A195821
Total number of parts that are not the smallest part in all partitions of n that do not contain 1 as a part.
1
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
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.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 19 2011
STATUS
approved