[seqfan] Re: Tatami

[Richard J. Mathar]

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