The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241640 Number of partitions p of n such that (number of even numbers in p) > (number of odd numbers in p). 6
 0, 0, 1, 0, 2, 0, 3, 1, 6, 4, 10, 11, 20, 23, 32, 44, 57, 77, 90, 129, 150, 208, 236, 334, 381, 522, 595, 803, 936, 1234, 1435, 1861, 2193, 2770, 3291, 4105, 4884, 6001, 7172, 8678, 10418, 12487, 14969, 17791, 21330, 25164, 30181, 35398, 42337, 49463, 59057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Each number in p is counted once, regardless of its multiplicity. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A241639(n) - A241638(n) for n >= 0. a(n) + A241636(n) + A241638(n) = A000041(n) for n >= 0. a(n) = Sum_{k<0} A242618(n,k). - Alois P. Heinz, May 19 2014 EXAMPLE a(6) counts these 3 partitions:  6, 42, 222. 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_ /; s0[p] < s1[p]], {n, 0, z}]  (* A241636 *) Table[Count[f[n], p_ /; s0[p] <= s1[p]], {n, 0, z}] (* A241637 *) Table[Count[f[n], p_ /; s0[p] == s1[p]], {n, 0, z}] (* A241638 *) Table[Count[f[n], p_ /; s0[p] >= s1[p]], {n, 0, z}] (* A241639 *) Table[Count[f[n], p_ /; s0[p] > s1[p]], {n, 0, z}]  (* A241640 *) CROSSREFS Cf. A241636, A241637, A241638, A241639. Sequence in context: A143351 A350962 A241644 * A158449 A106533 A192421 Adjacent sequences:  A241637 A241638 A241639 * A241641 A241642 A241643 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 08:57 EDT 2022. Contains 353940 sequences. (Running on oeis4.)