login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A241651 Number of partitions p of n such that 2*(number of even numbers in p) < (number of odd numbers in p). 5
0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 16, 22, 27, 38, 47, 66, 81, 112, 136, 187, 227, 301, 363, 473, 568, 727, 862, 1088, 1289, 1596, 1876, 2304, 2697, 3265, 3810, 4583, 5327, 6358, 7354, 8736, 10101, 11924, 13750, 16195, 18653, 21883, 25177, 29484, 33906 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..50.

FORMULA

a(n) = A241652(n) - A241653(n) for n >= 0.

a(n) + A241653(n) + A241655(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 4 partitions:  51, 33, 3111, 111111.

MATHEMATICA

z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0];

s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];

Table[Count[f[n], p_ /; 2 s0[p] < s1[p]], {n, 0, z}]  (* A241651 *)

Table[Count[f[n], p_ /; 2 s0[p] <= s1[p]], {n, 0, z}] (* A241652 *)

Table[Count[f[n], p_ /; 2 s0[p] == s1[p]], {n, 0, z}] (* A241653 *)

Table[Count[f[n], p_ /; 2 s0[p] >= s1[p]], {n, 0, z}] (* A241654 *)

Table[Count[f[n], p_ /; 2 s0[p] > s1[p]], {n, 0, z}]  (* A241655 *)

CROSSREFS

Cf. A241652, A241653, A241654, A241655.

Sequence in context: A238708 A266751 A063827 * A127217 A240735 A057042

Adjacent sequences:  A241648 A241649 A241650 * A241652 A241653 A241654

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)