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%I #8 Oct 14 2022 17:52:45
%S 1,1,2,1,2,3,0,2,3,4,0,0,3,4,5,0,0,0,4,5,6,0,0,0,0,5,6,7,0,0,0,0,0,6,
%T 7,8,0,0,0,0,0,0,7,8,9,0,0,0,0,0,0,0,8,9,10,0,0,0,0,0,0,0,0,9,10,11,0,
%U 0,0,0,0,0,0,0,0,10,11,12,0,0,0,0,0,0,0,0,0,0,11,12,13,0,0,0,0,0,0,0,0,0,0
%N A simple tridiagonal matrix.
%C Row sums are A008486 (coordination sequence for graphite net). Diagonal sums are A026741(n+1). Diagonals are A000027.
%F Number triangle where column k has g.f. (1+x+x^2)(k+1)x^k.
%e Triangle begins
%e 1;
%e 1, 2;
%e 1, 2, 3;
%e 0, 2, 3, 4;
%e 0, 0, 3, 4, 5;
%e 0, 0, 0, 4, 5, 6;
%e 0, 0, 0, 0, 5, 6, 7;
%e 0, 0, 0, 0, 0, 6, 7, 8;
%t Table[If[#<(n-2),0,#]&/@Range[n],{n,15}]//Flatten (* _Harvey P. Dale_, Oct 14 2022 *)
%Y Cf. A113126.
%K easy,nonn,tabl
%O 0,3
%A _Paul Barry_, Oct 14 2005
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