A194451 Partition numbers of positive integers and positive integers interleaved.

1, 1, 2, 2, 3, 3, 5, 4, 7, 5, 11, 6, 15, 7, 22, 8, 30, 9, 42, 10, 56, 11, 77, 12, 101, 13, 135, 14, 176, 15, 231, 16, 297, 17, 385, 18, 490, 19, 627, 20, 792, 21, 1002, 22, 1255, 23, 1575, 24, 1958, 25, 2436, 26, 3010, 27, 3718, 28, 4565, 29, 5604, 30

Offset

1,3

Comments

First differences of A194450. The length of the edges in a rectangular spiral whose vertices are the numbers A194450. The spiral contains exactly between its edges the successive last sections of the partitions of the natural numbers. For more information see A135010 and A138121.

Links

Table of n, a(n) for n=1..60.

Formula

a(2n-1) = p(n), a(2n) = n.

a(2n-1) = A000041(n), a(2n) = A000027(n).

a(2n-1) + a(2n) = A133041(n).

a(2n-1) - a(2n) = A000094(n+1).

a(2n-1) * a(2n) = A066186(n).

Crossrefs

Cf. A000041, A194450.

Sequence in context: A307993 A114092 A082500 * A059292 A115000 A036825

Adjacent sequences: A194448 A194449 A194450 * A194452 A194453 A194454

Keyword

nonn

Author

Omar E. Pol, Nov 01 2011

Status

approved