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A172008
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Number of minimal SNUSP programs using +, @ and # that yield n.
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1
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1, 1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 4, 2, 6, 2, 2, 2, 8, 8, 4, 2, 2, 2, 2, 2, 2, 6, 2, 2, 10, 10, 4, 2, 8, 8, 2, 2, 4, 8, 2, 2, 2, 6, 14, 2, 4, 4, 8, 8, 2, 4, 2, 4, 2, 2, 2, 4, 6, 6, 2, 2, 2, 2, 4, 4, 18, 18, 2, 2, 4, 2, 8, 2, 10, 2, 2, 2, 4, 4, 6, 4, 4, 4, 2, 2, 2, 4, 6, 6, 2, 2, 2, 8, 2, 2, 6, 6, 2
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OFFSET
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1,3
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COMMENTS
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Shortest SNUSP representation of a number using only + and @ is in A172005.
SNUSP is a programming language where each command is an individual letter. The three of concern here are + and @ and #. + increments the current data value, @ is a "subroutine call" and # is a "return". When an @ is encountered, a record of the location is put on a stack and execution continues. When a # is encountered, if there is a return point on the stack, the execution continues at that a single character beyond that return point. If there is no return point on the stack, execution terminates.
Thus "@@++#" would put the first two "@" return points on the stack, increment data twice, return from the second "@" to the last "+", increment the data once more, return from the first "@" to the first "+", increment the data two more times and finally terminate when it hits the "#" with no return points on the stack. The data is always initialized to zero so this effectively puts 5 into the data. In order to place a particular value into the data, there are one or more minimal strings of these characters. The i-th term of the sequence gives the number of minimal SNUSP programs using only these characters. After 2, all sequences end in either +++ or @++, which are equivalent, so all values above a(2) are even.
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LINKS
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EXAMPLE
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19 can be represented minimally in 6 ways using @, + and #: @+@+++++# +@@@++++# @++@@+++# @+@++@++# +@@@+@++# @++@@@++#. Thus a(19) = 6.
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MAPLE
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Darrell Plank (jar_czar(AT)msn.com), Jan 22 2010
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STATUS
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approved
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