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A194451
Partition numbers of positive integers and positive integers interleaved.
1
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.
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
Sequence in context: A307993 A114092 A082500 * A059292 A115000 A036825
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 01 2011
STATUS
approved