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A182911 Prime encoded sequence of generic integer partitions of n in the antilexicographic order of the partitions. 1
1, 2, 1, 1, 36, 1, 216, 900, 1, 1296, 5400, 44100, 27000, 7776, 32400, 264600, 5336100, 162000, 1323000, 46656, 194400, 810000, 1587600, 9261000, 32016600, 901800900, 972000, 7938000, 160083000, 279936, 1166400, 4860000, 9525600, 39690000, 55566000, 192099600, 1120581000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

By definition [1] is a generic partition and 0 has no generic partitions. For n > 1 a partition p of n is generic if it has not the form [1+r_1,r_2,..,r_k] or [r_1,r_2,..,r_k,1] for some partition [r_1,r_2,..,r_k] of n-1.

Encoding: The partition p = [p_1,..,p_k] is represented by the product_{i=1..k} prime_i ^ p_i. If n has generic partitions then these encodings are listed in the anti-lexicographic order of the partitions; if n has no generic partitions then this fact is represented by '1'.

Starting from generic partitions a table of all partitions can be built by two operations: appending '1' at the tail of a partition or adding 1 to the head of a partition (see the table at the link given).

A generic partition is a partition of the form [x,x,p_2,...,p_k-1,y] with y>1; in addition [1] is a generic partition by definition.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..47

Peter Luschny, Integer partition trees, OEIS wiki.

EXAMPLE

0:  {}                   -> 1

1:  {[1]}                -> 2^1 = 2

2:  {}                   -> 1

3:  {}                   -> 1

4:  {[22]}               -> 2^2*3^2 = 36

5:  {}                   -> 1

6:  {[33],[222]}         -> 2^3*3^3 = 216; 2^2*3^2*5^2 = 900

7:  {}                   -> 1

8:  {[44],[332],[2222]}  -> 1296, 5400, 44100

9:  {[333]}              -> 27000

MAPLE

a:= proc(n) local b, ll; b:=

      proc(n, i, l) local nl; nl:= nops(l);

        if n<0 then

      elif n=0 then ll:= ll,

               `if`(nl=0 or nl=1 and l[1]=1 or

                    nl>1 and l[-1]<>1 and l[1]=l[2],

                    mul(ithprime(t)^l[t], t=1..nl), NULL)

      elif i=0 then

      else b(n-i, i, [l[], i]), b(n, i-1, l)

        fi

      end;

      ll:= NULL; b(n, n, []);

     `if`(ll=NULL, 1, ll)

    end:

seq(a(n), n=0..15);

CROSSREFS

Cf. A046056, A053445.

Sequence in context: A147802 A093076 A132454 * A058293 A172092 A156888

Adjacent sequences:  A182908 A182909 A182910 * A182912 A182913 A182914

KEYWORD

nonn

AUTHOR

Peter Luschny, Jan 26 2011

STATUS

approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)