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Square array of numbers read by antidiagonals where T(n,k)=((k+3)(k+2)^n-2)/(k+1)
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%I #5 May 10 2013 12:45:29

%S 1,1,4,1,5,10,1,6,17,22,1,7,26,53,46,1,8,37,106,161,94,1,9,50,187,426,

%T 485,190,1,10,65,302,937,1706,1457,382,1,11,82,457,1814,4687,6826,

%U 4373,766,1,12,101,658,3201,10886,23437,27306,13121,1534,1,13,122,911,5266

%N Square array of numbers read by antidiagonals where T(n,k)=((k+3)(k+2)^n-2)/(k+1)

%C Nodes on a tree with degree k interior nodes and degree 1 boundary nodes.

%D L. He, X. Liu and G. Strang, (2003) Trees with Cantor Eigenvalue Distribution. Studies in Applied Mathematics 110 (2), 123-138

%F The total number of nodes on a tree with degree k interior nodes and degree 1 boundary nodes is given by N(k, r)=(k(k-1)^r-2))/(k-2).

%F G.f.: Sum_{k>=0} (1+x*y)/(1-x*y)/(1-(k+2)*x*y)*y^k. - _Vladeta Jovovic_, Dec 12 2003

%e Rows begin

%e 1 4 10 22 ...

%e 1 5 17 53 ...

%e 1 6 26 106 ...

%e 1 7 37 187 ...

%Y Rows include A033484, A048473, A020989, A057651, A061801, A090843.

%K easy,nonn,tabl

%O 0,3

%A _Paul Barry_, Dec 09 2003