login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239883 Number of strict partitions of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity. 2
1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 41, 55, 73, 99, 132, 177, 236, 313, 412, 540, 701, 904, 1159, 1473, 1861, 2336, 2915, 3615, 4463, 5478, 6698, 8152, 9887, 11944, 14391, 17280, 20703, 24739, 29506, 35115, 41730, 49501, 58650, 69389, 82009, 96807, 114175 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = number of strict partitions (that is, every part has multiplicity 1) of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity.  This sequence is nondecreasing, unlike A239881, of which it is a bisection; the other bisection is A239882.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

EXAMPLE

a(5) counts these 10 partitions of 11:  [11], [10,1], [9,2], [8,3], [8,1,2], [7,4], [6,5], [6,1,4], [6,3,2], [4,5,2].

MATHEMATICA

d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p[n_] := p[n] = Select[d[n], Abs[Count[#, _?OddQ] - Count[#, _?EvenQ]] <= 1 &]; t =  Table[p[n], {n, 0, 12}]

TableForm[t] (* shows the partitions *)

u = Table[Length[p[2 n + 1]], {n, 0, 20}]  (* A239883 *)

(* Peter J. C. Moses, Mar 10 2014 *)

CROSSREFS

Cf. A239881, A239882, A239872.

Sequence in context: A008628 A038499 A118199 * A088318 A038083 A238863

Adjacent sequences:  A239880 A239881 A239882 * A239884 A239885 A239886

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 29 2014

EXTENSIONS

More terms from Alois P. Heinz, Mar 31 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 March 19 00:14 EDT 2019. Contains 321306 sequences. (Running on oeis4.)