[seqfan] Re: Guess the Triangle

[Ron Hardin]

The following matches four leading points found for row 7 (889 10199 57337 
218743)
(assuming 14, 7 and 84=84)

a(k) = 1
a(k) = 4*k + 2
a(k) = 6*k^2 + 12*k + 3
a(k) = 8*k^3 + 24*k^2 + 24*k + 4
a(k) = 10*k^4 + 40*k^3 + 60*k^2 + 40*k + 5
a(k) = 12*k^5 + 60*k^4 + 120*k^3 + 120*k^2 + 60*k + 6
a(k) = 14*k^6 + 84*k^5 + 210*k^4 + 280*k^3 + 210*k^2 + 84*k + 7

 rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: Ron Hardin <rhhardin at att.net>
> To: seqfan at list.seqfan.eu
> Sent: Thu, March 28, 2013 7:32:31 PM
> Subject: [seqfan] Guess the Triangle
> 
> /tmp/dfs
> T(n,k)=Number of idempotent nXn 0..k matrices of rank  n-1
> 
> Rows n=1..6 match
> a(k) = 1
> a(k) = 4*k + 2
> a(k) = 6*k^2 +  12*k + 3
> a(k) = 8*k^3 + 24*k^2 + 24*k + 4
> a(k) = 10*k^4 + 40*k^3 + 60*k^2  + 40*k + 5
> a(k) = 12*k^5 + 60*k^4 + 120*k^3 + 120*k^2 + 60*k +  6
> 
> 
> (rank n-1 = trace n-1)
> 
> rhhardin at mindspring.com
> rhhardin at att.net (either)
> 
> 
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