[seqfan] An Audiosurf-based sequence
kimpire at yahoo.com
Wed Aug 26 11:57:54 CEST 2020
In the spirit of such esoteric game-based sequences as A306221, A060225, and A054863, I looked into the game Audiosurf, in which the player collects colored blocks while driving down a track. I was curious as to whether the points scored for matches of different sizes had any kind of underlying logic.
The base point scores for sets of purple-colored blocks are as follows (starting with a set of 3 blocks and incrementing by 1):36 73 119 174 236 303 375 451 531 612 695 775 854 929 1001 1070 1136 1199 1260
For which superseeker returned this:
>The gfun package's guessgf function identified thesepossible generating functions.>Warning! These may only be approximations!
> revogf RootOf(-y+(3*y+36)*_Z+(-3*y-35)*_Z^2+(y+8)*_Z^3-2*_Z^5-2*_Z^6-_Z^8-3*_Z^10+_Z^11-5*_Z^12+2*_Z^13-3*_Z^14+_Z^15)
Other colored blocks give points as a simple whole-number multiple of the above sequence (for example, red blocks are worth 8 times as many points) so those are not of separate interest. However, when playing in Mono mode, the score is multiplied by 3.33 and then rounded:
120 243 398 580 786 1010 1251 1504 1768 2041 2316 2585 2846 3097 3337 3567 3787 3997 4200
I don't expect either of these sequences to be worth adding, but I thought I'd throw it out there in case any of you come up with something.
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