The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A241740 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A241740

Number of partitions p of n such that (number of numbers in p of form 3k+2) < (number of numbers in p of form 3k).
(history; published version)

#5 by N. J. A. Sloane at Tue May 06 15:05:32 EDT 2014

STATUS

proposed

approved

#4 by Clark Kimberling at Sun May 04 09:37:45 EDT 2014

STATUS

editing

proposed

#3 by Clark Kimberling at Mon Apr 28 15:18:08 EDT 2014

FORMULA

a(n) + A241741(n) + A241842(n) = A000041(n) for n >= 0.

#2 by Clark Kimberling at Mon Apr 28 12:48:06 EDT 2014

NAME

allocated for Clark KimberlingNumber of partitions p of n such that (number of numbers in p of form 3k+2) < (number of numbers in p of form 3k).

DATA

0, 0, 0, 1, 1, 1, 3, 4, 4, 7, 10, 12, 17, 24, 30, 40, 53, 70, 90, 118, 152, 194, 244, 316, 396, 497, 626, 784, 960, 1202, 1483, 1816, 2230, 2738, 3312, 4042, 4908, 5922, 7141, 8627, 10327, 12388, 14832, 17703, 21075, 25120, 29795, 35321, 41822, 49439, 58286

OFFSET

0,7

COMMENTS

Each number in p is counted once, regardless of its multiplicity.

FORMULA

a(n) + A241741(n) +A241842(n) = A000041(n) for n >= 0.

EXAMPLE

a(8) counts these 4 partitions: 611, 431, 3311, 311111.

MATHEMATICA

z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];

Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}] (* A241740 *)

Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)

Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}] (* A241742 *)

CROSSREFS

Cf. A241737, A241741, A241741, A241743.

KEYWORD

allocated

nonn,easy

AUTHOR

Clark Kimberling, Apr 28 2014

STATUS

approved

editing

#1 by Clark Kimberling at Sun Apr 27 17:31:15 EDT 2014

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved