A035399 -id:A035399 - cp's OEIS frontend

A035400 Differences of A035399.

1, 1, 2, 1, 2, 1, 4, 1, 1, 5, 1, 1, 3, 6, 1, 1, 2, 1, 10, 1, 1, 2, 1, 3, 14, 1, 1, 2, 1, 2, 1, 5, 17, 1, 1, 2, 1, 2, 1, 5, 1, 8, 20, 1, 1, 2, 1, 2, 1, 4, 1, 1, 6, 3, 33, 1, 1, 2, 1, 2, 1, 4, 1, 1, 6, 1, 3, 8, 1, 44, 1, 1, 2, 1, 2, 1, 4, 1, 1, 5, 1, 1, 3, 7, 2, 1, 14, 53, 1, 1, 2, 1, 2, 1, 4, 1, 1, 5, 1

Offset: 1

Olivier Gérard

nonn

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

Cf. A000009, A035399.

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

Original entry on oeis.org

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

Wouter Meeussen, Feb 13 2011

nonn

			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.

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

Cf. A186131, A035399.

First differences give A186203.

<?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 ]

A186131 Positions of the odd partitions of (2k) in reverse lexicographic order converge to this limiting sequence.

Original entry on oeis.org

2, 5, 7, 13, 16, 19, 31, 34, 38, 41, 45, 68, 71, 76, 79, 86, 88, 92, 97, 140, 143, 148, 151, 159, 162, 164, 168, 181, 184, 189, 195, 273, 276, 281, 284, 293, 296, 298, 302, 317, 319, 326, 329, 334, 353, 356, 360, 366, 373, 509, 512, 517, 520, 529, 532, 534, 538, 554, 557, 559, 566, 569, 574, 601

Offset: 1

Wouter Meeussen, Feb 13 2011

nonn

			The odd partitions of (2*4) occur at positions 2, 5, 7, 14, 17 and 22. For (2*5) they occur at 2, 5, 7, 13, ... so for k=5 only the first three terms have stabilized, giving a(1) = 2, a(2) = 5, and a(3) = 7.

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

Cf. A186130, A035399.

First differences give A186204.

<?EvenQ], 1]], {n, 36, 36+2, 2}]; {{diffat}}=Position[Take[Last[it], Length[First[it] ] ] - First[it] , a /; (a!=0), 1, 1]; Take[First[it], diffat -1 ]

A308916 Irregular triangular array: row n shows positions of strict partitions of n among all partitions of n, using Mathematica ordering.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 6, 1, 2, 3, 5, 6, 1, 2, 3, 5, 6, 9, 1, 2, 3, 5, 6, 8, 9, 14, 1, 2, 3, 5, 6, 8, 9, 14, 15, 23, 1, 2, 3, 5, 6, 8, 9, 13, 14, 15, 21, 24, 1, 2, 3, 5, 6, 8, 9, 13, 14, 15, 21, 22, 25, 33, 34, 1, 2, 3, 5, 6, 8, 9, 13, 14, 15

Offset: 1

Clark Kimberling, Jun 30 2019

			1
1
1   2
1   2
1   2   3
1   2   3   6
1   2   3   5   6
1   2   3   5   6   9
1   2   3   5   6   8   9   14
1   2   3   5   6   8   9   14   15   23
Strict partitions of 6: {6}, {5, 1}, {4, 2}, {3, 2, 1}, which occupy positions 1,2,3,6 in the ordering of all partitions of 6: {6}, {5, 1}, {4, 2}, {4, 1, 1}, {3, 3}, {3, 2, 1}, {3, 1, 1, 1}, {2, 2, 2}, {2, 2, 1, 1}, {2, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}

Cf. A000009, A000041, A118457, A035399.

p[n_] := IntegerPartitions[n];
d[n_] := Select[p[n], Max[Length /@ Split@#] == 1 &];
t = Table[Flatten[Table[Position[p[n], d[n][[k]]], {k, 1, Length[d[n]]}]], {n, 1, 15}]
Flatten[t]  (* A308916, sequence *)

cp's OEIS Frontend

A035400 Differences of A035399.

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

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Keywords

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Mathematica

A186131 Positions of the odd partitions of (2k) in reverse lexicographic order converge to this limiting sequence.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A308916 Irregular triangular array: row n shows positions of strict partitions of n among all partitions of n, using Mathematica ordering.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica