Talk:9 billion names of God the integer

task clarification

I presume from the task requirement that the output is to more-or-less look like the (partial) number triangle shown, that is, a symmetric isosceles triangle in the manner of Pascal's triangle.   Producing a left-justified triangle doesn't look or feel right. -- Gerard Schildberger (talk) 20:35, 2 May 2013 (UTC)

That's really kinda silly, y'know? And you can't do it perfectly symmetrical anyway unless you can half-space. In any case, it's arguably not a symmetrical triangle after row 4... --TimToady (talk) 01:57, 3 May 2013 (UTC)

More to the point, the algorithm isn't symmetrical; the values are not derived from the two values above. The visual identity with Pascal's triangle is completely vacuous, and the ancestors the algorithm is visiting are, in fact, easier to see with the left-justified form! --TimToady (talk) 02:09, 3 May 2013 (UTC)

Sorry, I didn't mean to get anybody all worked up and start with the name calling.   I meant to say isosceles triangle, not symmetric isosceles.   I never intended to imply that the values in the triangle were (perfectly?) symmetrical.   The visual comparison with Pascal's triangle was referring to the shape, not the values of the numbers in the triangle, and not also, of course, how the numbers are derived.   Indeed, the task's author chose to show the first ten rows in an isolsceles triangle shape, and I followed (or mimiced) that manner. -- Gerard Schildberger (talk) 23:15, 3 May 2013 (UTC)

The 2nd part of the task's requirement states that the   integer partition function   (IPF)   is the same as the sum of the n-th row of the number triangle (constructed above), and furthermore, this is to be demonstrated.   None of the examples (so far) has shown the last line of any of the P(23), P(123), P(1234), and P(12345) for this purpose.   Indeed, it's doable, but the last line of the bigger number triangles would be huge.   Are the program examples supposed to sum the last row of the number triangle   and   verify via calculating the IPF via formulaic means? -- Gerard Schildberger (talk) 20:49, 2 May 2013 (UTC)

The origional task description did not mention the IPF and called for 25 lines of the triangle. The purpose of G(n) is to show that you can generate the nth line of this triangle without having to display all 12345 elements of it. Other formulations are interesting but not solutions to this task. I have added a child task http://rosettacode.org/wiki/9_billion_names_of_God_the_integer/Worship_of_false_idols where I think that these related triangles should be discussed.--Nigel Galloway (talk) 13:12, 3 May 2013 (UTC)

Note that http://rosettacode.org/wiki/9_billion_names_of_God_the_integer#Full_Solution does exactly that which you say no example does.--Nigel Galloway (talk) 13:12, 3 May 2013 (UTC)

I don't see where it displays the last line of the P(23), P(123), P(1234), and P(12345) number triangles.   Most of the programming examples did show the sums of the last lines, of course. -- Gerard Schildberger (talk) 17:26, 3 May 2013 (UTC)

generating function for P(n)

If the formula shown under the C example is Euler's generating function, is it missing a   ½   multiplier? -- Gerard Schildberger (talk) 23:35, 2 May 2013 (UTC)

It's not a generating function, but yes, both the subscripts in the displayed equation were missing a "/2". --Ledrug (talk) 03:15, 3 May 2013 (UTC)