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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239880 Number of strict partitions of n having an ordering in which no parts of equal parity are juxtaposed and the first and last terms have the same parity. 3
0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 10, 11, 14, 15, 19, 22, 26, 30, 35, 42, 47, 56, 62, 76, 83, 100, 108, 132, 142, 171, 184, 222, 239, 284, 306, 363, 394, 460, 500, 581, 636, 730, 802, 914, 1010, 1139, 1262, 1415, 1577, 1753, 1956, 2163, 2423, 2663 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

A strict partition is one in which every part has multiplicity 1.

a(n) = A240021(n,-1) + A240021(n,1). - Alois P. Heinz, Apr 02 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

a(12) counts these 7 partitions:  [12], [9,2,1], [3,8,1], [7,4,1], [7,2,3], [5,6,1], [5,4,3].

MAPLE

b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or

       abs(t)-n>1, 0, `if`(n=0, abs(t), b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..80);  # Alois P. Heinz, Apr 02 2014

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[n]], {n, 0, 60}]  (* A239880 *)

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

b[n_, i_, t_] := b[n, i, t] = If[n > i*(i+1)/2 || Abs[t]-n>1, 0, If[n==0, Abs[t], b[n, i-1, t] + If[i>n, 0, b[n-i, i-1, t + (2*Mod[i, 2]-1)]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, Aug 29 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A239833, A239835, A239881.

Sequence in context: A029019 A040039 A008667 * A240862 A177716 A109763

Adjacent sequences:  A239877 A239878 A239879 * A239881 A239882 A239883

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 29 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)