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Tridiagonal matrix associated with coordination sequences.
0

%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