[Jprogramming] Takes from a mystery sequence

[Kip Murray]

Oh, this is good!  (I had in mind something involving differences and 
interpolation that I saw in Lester R. Ford's great text Differential Equations.)

Thanks, Raul!

I hope you noticed Pascal's triangle lurking in my puzzles.  Verb (iii0 + iii1) 
involved in conventional notation (1+x)^3 , and (v0+v1) , (1-x)^5 as the 
"generating functions".

Kip


Raul Miller wrote:
> On Tue, Aug 18, 2009 at 5:27 PM, Kip Murray<km at math.uh.edu> wrote:
>>    (v0 ,: v1) 10
>> 1  6  31   76  141   226   331   456    601    766  <-- 10 from first sequence
>> 0 _6 _32 _108 _384 _1250 _3456 _8232 _17408 _33534  <-- 10 from second sequence
>>
>> Have you seen a polynomial-fitting verb for data such as iii0 10 and iii1 10 ?
> 
>    (%. ^/~@i.@#) x:1  6  31   76  141   226   331   456    601    766
> 1 _5 10 0 0 0 0 0 0 0
>    1 _5 10 p. i. 10
> 1 6 31 76 141 226 331 456 601 766
>    (%. ^/~@i.@#) x:0 _6 _32 _108 _384 _1250 _3456 _8232 _17408 _33534
> 0 0 0 _10 5 _1 0 0 0 0
> 
>> Did you look at (iii0 + iii1) 10 ?
> 
> If I recall correctly, it was
>    3 ^~1+i.10
>