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%I #6 Jan 30 2021 08:44:11
%S 1,2,2,1,4,3,0,2,6,4,0,0,3,8,5,0,0,0,4,10,6,0,0,0,0,5,12,7,0,0,0,0,0,
%T 6,14,8,0,0,0,0,0,0,7,16,9,0,0,0,0,0,0,0,8,18,10,0,0,0,0,0,0,0,0,9,20,
%U 11,0,0,0,0,0,0,0,0,0,10,22,12,0,0,0,0,0,0,0,0,0,0,11,24,13,0,0,0,0,0,0,0
%N Tridiagonal matrix associated with coordination sequences.
%C Coefficient array of expansion of ((1+x)/(1-r*x))^2, or self-convolution of coordination sequence for the infinite tree with valency r. Row sums are A008574, (coordination sequence for square lattice). Diagonal sums are A000027.
%F Column k has g.f. (1+x)^2*(k+1)x^k.
%e Triangle begins
%e 1;
%e 2, 2;
%e 1, 4, 3;
%e 0, 2, 6, 4;
%e 0, 0, 3, 8, 5;
%e 0, 0, 0, 4, 10, 6;
%e 0, 0, 0, 0, 5, 12, 7;
%Y Cf. A113070, A113071.
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Oct 14 2005
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