[seqfan] Re: Rank of n in the Odd/Even sequence

[Prof. Dr. Alois Heinz]

Eric Angelini schrieb:

> Is the hereunder idea 'chaff' ?

Yes, it is.

>I have computed this array yesterday (by hand):
>
> S(1) =  1, 1,  6,   58,     5829,    58292915, ...
> S(2) =  2, 1, 11, 1056, 10555528, ...
> S(3) =  3, 2, 16, 1608, 16080804, ...
> S(4) =  4, 2, 21, 2111, 21106056, ...
> S(5) =  5, 3, 27, 2664, 26636332, ...
> S(6) =  6, 3, 32, 3166, 31661583, ...
> S(7) =  7, 4, 37, 3719, 37186860, ...
> S(8) =  8, 4, 42, 4221, 42212111, ...
> S(9) =  9, 5, 48, 4774, 47742387, ...     
>S(10) = 10, 5, 53, 5277, 52767639, ...
>
>Could someone extend this array (to the right) -- or at least S(1)?
>
>  
>
But with the help of a tiny Maple Program ...

rank:= n-> `if` (type(n, 'even'), n/2, (n+1)/2);
a := proc (n,k) option remember;
 if n=1 then k
        else rank (parse (cat(seq(a(j,k), j=1..n-1))))
 fi
end;


for k from 1 to 10 do  lprint (seq(a(n,k), n=1..7)) od ;

1, 1, 6, 58, 5829, 58292915, 5829291479146458
2, 1, 11, 1056, 10555528, 1055552805277764, 10555528052777640527776402638882
3, 2, 16, 1608, 16080804, 1608080408040402, 16080804080404020804040204020201
4, 2, 21, 2111, 21106056, 2110605560553028, 21106055605530281055302780276514
5, 3, 27, 2664, 26636332, 2663633213318166, 26636332133181661331816606659083
6, 3, 32, 3166, 31661583, 3166158315830792, 31661583158307916583079157915396
7, 4, 37, 3719, 37186860, 3718685968593430, 37186859685934301859342984296715
8, 4, 42, 4221, 42212111, 4221211071106056, 42212110711060557110605535553028
9, 5, 48, 4774, 47742387, 4774238723871194, 47742387238711937387119361935597
10, 5, 53, 5277, 52767639, 5276763876383820, 
52767638763838197638381938191910

seq (a(n,1), n=1..10);
 1, 1, 6, 58, 5829, 58292915, 5829291479146458,
 58292914791464577914645739573229,
 5829291479146457791464573957322929146457395732288957322869786615,
 58292914791464577914645739573229291464573957322889573228697866147914645739573228895732286978661464573228697866144478661434893308


With regards, Alois