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

0,5

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.

Links

Table of n, a(n) for n=0..77.

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.

Crossrefs

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

Sequence in context: A281648 A353154 A325962 * A239233 A051704 A049689

Adjacent sequences: A210448 A210449 A210450 * A210452 A210453 A210454

Keyword

nonn

Author

Omar E. Pol, Jan 27 2013

Status

approved