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%I #4 Mar 30 2012 18:51:35
%S 1,2,1,2,3,1,2,5,4,1,2,7,10,5,1,2,9,22,17,6,1,2,11,46,53,26,7,1,2,13,
%T 94,161,106,37,8,1,2,15,190,485,426,187,50,9,1,2,17,382,1457,1706,937,
%U 302,65,10,1,2,19,766,4373,6826,4687,1814,457,82,11,1,2,21,1534,13121
%N Square array read by antidiagonals of base n numbers written as 122...222 with k 2's (and a suitable interpretation for n=0, 1 or 2).
%C Start with a node; step one is to connect that node to n+1 new nodes so that it is of degree n+1; further steps are to connect each existing node of degree 1 to n new nodes so that it is of degree n+1; T(n,k) is the total number of nodes after k steps.
%F T(n, k) =((n+1)*n^k-2)/(n-1) [with T(1, k)=2k+1] =n*T(n, k-1)+2 =(n+1)*T(n, k-1)-n*T(n, k-2) =T(n, k-1)+(1+1/n)*n^k =A055129(k, n)+A055129(k-1, n). Coefficient of x^k in expansion of (1+x)/((1-x)(1-nx)).
%e Rows start: 1,2,2,2,2,2,...; 1,3,5,7,9,11,...; 1,4,10,22,46,94,...; 1,5,17,53,161,485,... T(3,2) =122 base 3 =17.
%Y Rows include A040000, A005408, A033484, A048473, A020989, A057651, A061801 etc. For negative n (not shown) absolute values of rows would effectively include A000012, A014113, A046717.
%K base,nonn,tabl
%O 0,2
%A _Henry Bottomley_, Feb 06 2002
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