A186130 Positions of the odd partitions of (2k+1) in reverse lexicographic order converge to this limiting sequence.

1, 4, 9, 12, 21, 24, 26, 30, 47, 50, 52, 59, 62, 67, 99, 102, 104, 110, 113, 116, 126, 129, 133, 139, 197, 200, 202, 208, 211, 214, 227, 231, 234, 238, 254, 256, 260, 265, 272, 375, 378, 380, 386, 389, 392, 404, 407, 411, 414, 418, 440, 443, 450, 452, 456, 461, 486, 489, 494, 500, 508, 686, 689, 691

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

The odd partitions of (2*4+1) occur at positions 1, 4, 9, 12, 19, 21, 25, and 30. For (2*5+1) they occur at 1, 4, 9, 12, 20, ..., so for k=5 only four terms have stabilized, giving a(1) = 1, a(2) = 4, a(3) = 9, and a(4) = 12.

Mathematica

<<DiscreteMath`Combinatorica`;
it=Table[Flatten[Position[Partitions[n], q_List/;  FreeQ[q, _?EvenQ], 1]], {n, 39, 39+2, 2}]; {{diffat}}=Position[Take[Last[it], Length[First[it] ] ] - First[it] , a_ /; (a!=0), 1, 1]; Take[First[it], diffat -1 ]

Crossrefs

Cf. A186131, A035399.

First differences give A186203.

Sequence in context: A256887 A119640 A332225 * A051233 A124623 A220195

Adjacent sequences: A186127 A186128 A186129 * A186131 A186132 A186133

Keyword

nonn

Author

Wouter Meeussen, Feb 13 2011

Status

approved