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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. 1
2, 5, 20, 149, 1852, 34354, 873386, 28671789, 1166062774, 56973937168, 3266313635225, 215667757729237 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A118181 A140988 A136650 * A111885 A159320 A184730
KEYWORD
nonn,hard,more
AUTHOR
Gil Dogon, Sep 27 2013
STATUS
approved

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Last modified March 3 12:51 EST 2024. Contains 370512 sequences. (Running on oeis4.)