

A048249


Number of distinct values produced from sums and products of n unity arguments.


1



1, 2, 3, 4, 6, 9, 11, 17, 23, 30, 44, 60, 80, 114, 156, 212, 296, 404, 556, 770, 1065, 1463, 2032, 2795, 3889, 5364, 7422, 10300, 14229, 19722, 27391, 37892, 52599, 73075, 101301, 140588, 195405, 271024, 376608, 523518, 726812, 1010576
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OFFSET

1,2


COMMENTS

Values listed calculated by exhaustive search algorithm.
For n+1 operands (n operations) there are (2n)!/((n!)((n+1)!)) possible postfix forms over a single operator. For each such form, there are 2^n ways to assign 2 operators (here, sum and product). Calculate results and eliminate duplicates.


LINKS

Table of n, a(n) for n=1..42.
Index to sequences related to the complexity of n
Index entries for similar sequences


FORMULA

Equals partial sum of "number of numbers of complexity n" (A005421).  Jonathan Vos Post, Apr 07 2006


EXAMPLE

a(3)=3 since (in postfix): 111** = 11*1* = 1, 111*+ = 11*1+ = 111+* = 11+1* = 2 and 111++ = 11+1+ = 3. Note that at n=7, the 11 possible values produced are the set {1,2,3,4,5,6,7,8,9,10,12}. This is the first n for which there are "skipped" values in the set.


CROSSREFS

Sequence in context: A007210 A198394 A035947 * A018471 A240307 A128166
Adjacent sequences: A048246 A048247 A048248 * A048250 A048251 A048252


KEYWORD

nonn,nice


AUTHOR

Tony Bartoletti


EXTENSIONS

More terms from David W. Wilson, Oct 10 2001


STATUS

approved



