A194450 Vertex number of a rectangular spiral which contains exactly between its edges the successive shells of the partitions of the positive integers.

0, 1, 2, 4, 6, 9, 12, 17, 21, 28, 33, 44, 50, 65, 72, 94, 102, 132, 141, 183, 193, 249, 260, 337, 349, 450, 463, 598, 612, 788, 803, 1034, 1050, 1347, 1364, 1749, 1767, 2257, 2276, 2903, 2923, 3715, 3736, 4738, 4760, 6015, 6038, 7613, 7637, 9595

Offset

0,3

Comments

First differences give A194451, the length of the edges of the spiral. For more information see A135010 and A138121.

Links

Table of n, a(n) for n=0..49.

Formula

a(2n-1) = A026905(n) + A000217(n) - n, if n >= 1.

a(2n) = A026905(n) + A000217(n), if n >= 1.

Crossrefs

Cf. A000041, A000217, A006128, A026905, A066186, A135010, A138121, A138879, A138880, A182703, A182994, A182995, A194451.

Sequence in context: A090178 A080548 A338200 * A080556 A229093 A342371

Adjacent sequences: A194447 A194448 A194449 * A194451 A194452 A194453

Keyword

nonn

Author

Omar E. Pol, Nov 01 2011

Status

approved