A210451 n minus the number of parts in the n-th region of the set of partitions of j, if 1<=n<=A000041(j), with a(0) = 0.

0, 0, 0, 0, 3, 0, 5, 0, 7, 7, 9, 0, 11, 11, 13, 0, 15, 15, 17, 15, 19, 20, 0, 22, 22, 24, 22, 26, 26, 28, 0, 30, 30, 32, 30, 34, 35, 30, 37, 37, 39, 40, 0, 42, 42, 44, 42, 46, 46, 48, 42, 50, 51, 50, 53, 54, 0, 56, 56, 58, 56, 60, 61, 56, 63, 63, 65, 66, 56, 68, 68, 70, 68, 72, 72, 74, 75, 0

Offset: 0

Author

Omar E. Pol, Jan 27 2013

Keywords

• nonn

Comments

a(0) = 0 iff n is a partition number A000041, n >= 1.

a(n) is also the number of zeros in the n-th row of triangle A186114 and also of triangle A193870, n >= 1.

a(n) is also the value of the index "i" mentioned in the definition of "regions of the set of partitions" in A206437.

Crossrefs

Cf. A135010, A141285, A194446, A186114, A193870, A194447, A206437.

Formula

a(n) = n - A194446(n) = n - A141285(n) + A194447(n).

a(n+1) = a(n+2) = n, if a(n) = 0 and n >= 7.