A229662 The number of subsets of integers of cardinality n, produced as the steps in a computation starting with 1 and using the operations of multiplication, addition, or subtraction.

2, 5, 20, 149, 1852, 34354, 873386, 28671789, 1166062774, 56973937168, 3266313635225, 215667757729237

Offset

1,1

Comments

A straight-line program (SLP) is a sequence that starts at 1 and has each entry obtained from two preceding entries by addition, multiplication, or subtraction. The length of the SLP is defined as that of the sequence without the first 1. An SLP is said to be reduced if there is no repetition in the sequence. Two SLPs are considered equivalent if their sequence defines the same set of integers. This OEIS sequence gives the number of reduced SLPs with n steps.

Links

Table of n, a(n) for n=1..12.

Formula

a(n) >= a(n-1) * 2 * (n-1) and a(2)=5 Hence a(n) >= 5*2^(n-2)*(n-1)! .

Example

a(1) = 2 and the SLPs are (1,2) (1,0)
a(2) = 5 and the SLPs are (1,2,3) (1,2,4) (1,2,-1) (1,0,-1) (1,0,2)

Crossrefs

Cf. A229673, A214872, A216999, A173419, A141414.

Sequence in context: A118181 A140988 A136650 * A111885 A159320 A184730

Adjacent sequences: A229659 A229660 A229661 * A229663 A229664 A229665

Keyword

nonn,hard,more

Author

Gil Dogon, Sep 27 2013

Status

approved