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A240452 Number of partitions p of n such that (sum of parts with multiplicity 1) >= (sum of all other parts). 5
1, 1, 1, 2, 3, 4, 6, 8, 13, 17, 22, 28, 43, 55, 71, 87, 124, 153, 202, 243, 332, 401, 511, 608, 828, 984, 1236, 1458, 1903, 2245, 2826, 3301, 4245, 4963, 6119, 7108, 9064, 10508, 12837, 14834, 18584, 21442, 26150, 30028, 37139, 42599, 51356, 58742, 72370 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..48.

FORMULA

a(n) + A240449(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 6 partitions:  6, 51, 42, 411, 321, 3111.

MATHEMATICA

z = 30; p[n_] := p[n] = IntegerPartitions[n]; f[p_] := f[p] = First[Transpose[p]];

ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] < n &], {n, 0, z}]] (* shows the partitions *)

Map[Length, t]  (* A240448 *)

ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] <= n &], {n, 0, z}]] (* shows the partitions *)

Map[Length, t]  (* A240449 *)

ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] == n &], {n, 0, z}]] (* shows the partitions *)

Map[Length, t]  (* A240447 with alternating 0s *)

ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] > n &], {n, 0, z}]] (* shows the partitions *)

Map[Length, t]  (* A240451 *)

ColumnForm[t = Table[Select[p[n], 2 Total[f[Select[#, Last[#] == 1 &] /. {} -> {{0, 0}}]] &[Tally[#]] >= n &], {n, 0, z}]] (* shows the partitions *)

Map[Length, t]  (* A240452 *)

(* Peter J. C. Moses, Apr 02 2014 *)

CROSSREFS

Cf. A240448, A240447, A240449, A240451, A000041.

Sequence in context: A294342 A094372 A039880 * A263359 A246905 A000029

Adjacent sequences:  A240449 A240450 A240451 * A240453 A240454 A240455

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 05 2014

STATUS

approved

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Last modified February 19 22:04 EST 2018. Contains 299357 sequences. (Running on oeis4.)