30 Dec '19 19:15>7 edits
I would like the equation for this number pattern generated by one of my computer programs that generated it via an extremely complex maths iteration;
1, 2, 5, 8, 13, 19, 25, 33, 42, 51, 62, 74, 86, 100, 115, 130, 147, 165, ...
It was generated by inputting an integer c and outputting an integer s so that they correspond thus;
If c=1 then s=1
If c=2 then s=2
If c=3 then s=5
If c=4 then s=8
If c=5 then s=13
If c=6 then s=19
If c=7 then s=25
If c=8 then s=33
If c=9 then s=42
If c=10 then s=51
If c=11 then s=62
If c=12 then s=74
If c=13 then s=86
If c=14 then s=100
If c=15 then s=115
If c=16 then s=130
If c=17 then s=147
If c=18 then s=165
My computer program cannot do it for c over 18 because if c>18 then it cannot cope with the huge factorials in the iteration.
I tried WolfranAlpha this sequence and it showed me both some more numbers continuing in that sequence and an equation for it but that equation doesn't make any sense to me because it is an equation with letter z and I don't get what that z is supposed to be but here is that equation;
G_n(a_n)(z) = (z^5 - 2 z^4 + z^3 - 2 z^2 - 1)/((z - 1)^3 (z^2 + z + 1))
I tried various integer values for z above but it doesn't seen to output integers with that so don't get it.
So what does that z represent and that "G_n(a_n)(z)" mean?
The equation is no good to me if I don't understand how to use it.
Anyone?
1, 2, 5, 8, 13, 19, 25, 33, 42, 51, 62, 74, 86, 100, 115, 130, 147, 165, ...
It was generated by inputting an integer c and outputting an integer s so that they correspond thus;
If c=1 then s=1
If c=2 then s=2
If c=3 then s=5
If c=4 then s=8
If c=5 then s=13
If c=6 then s=19
If c=7 then s=25
If c=8 then s=33
If c=9 then s=42
If c=10 then s=51
If c=11 then s=62
If c=12 then s=74
If c=13 then s=86
If c=14 then s=100
If c=15 then s=115
If c=16 then s=130
If c=17 then s=147
If c=18 then s=165
My computer program cannot do it for c over 18 because if c>18 then it cannot cope with the huge factorials in the iteration.
I tried WolfranAlpha this sequence and it showed me both some more numbers continuing in that sequence and an equation for it but that equation doesn't make any sense to me because it is an equation with letter z and I don't get what that z is supposed to be but here is that equation;
G_n(a_n)(z) = (z^5 - 2 z^4 + z^3 - 2 z^2 - 1)/((z - 1)^3 (z^2 + z + 1))
I tried various integer values for z above but it doesn't seen to output integers with that so don't get it.
So what does that z represent and that "G_n(a_n)(z)" mean?
The equation is no good to me if I don't understand how to use it.
Anyone?