[seqfan] Re: Tatami

Richard J. Mathar mathar at mpia-hd.mpg.de
Thu Mar 24 16:18:31 CET 2016

```There are two different formulas now in the arena. The earlier one of
http://list.seqfan.eu/pipermail/seqfan/2016-February/016160.html
S_3 = 2* sum_{k=0.. (n-3)/4} ((n+3)/2-k)* binomial( (n-3)/2-k,k)
and the later one in http://list.seqfan.eu/pipermail/seqfan/2016-March/016243.html
with a different numerator in the binomial term:
S_3 = 2* sum_{k=0.. (n-3)/4} ((n+3)/2-k)* binomial( (n-1)/2-k,k)

The first formula gives the sequence

2, 10, 18, 38, 72, 136, 250, 454, 814, 1446, 2548...

The second formula gives the sequence

2, 10, 18, 46, 82, 168, 300, 562, 996, 1790, 3140..

S1 := proc(n)
add( ((n+1)/2-k)*binomial((n-1)/2-k,k),k=0..(n-1)/4) ;
%*2 ;
end proc:
S3 := proc(n)
# http://list.seqfan.eu/pipermail/seqfan/2016-February/016160.html
add( ((n+3)/2-k)*binomial((n-3)/2-k,k),k=0..(n-3)/4) ;
# http://list.seqfan.eu/pipermail/seqfan/2016-March/016243.html
add( ((n+3)/2-k)*binomial((n-1)/2-k,k),k=0..(n-3)/4) ;
%*2 ;
end proc:
seq(S1(2*k+1)+S3(2*k+1),k=0..10) ;

Richard
```

More information about the SeqFan mailing list