%I #2 Mar 30 2012 18:59:12

%S 1,1,2,1,2,3,1,2,3,4,0,2,3,4,5,0,0,3,4,5,6,0,0,0,4,5,6,7,0,0,0,0,5,6,

%T 7,8,0,0,0,0,0,6,7,8,9,0,0,0,0,0,0,7,8,9,10,0,0,0,0,0,0,0,8,9,10,11,0,

%U 0,0,0,0,0,0,0,9,10,11,12,0,0,0,0,0,0,0,0,0,10,11,12,13,0,0,0,0,0,0,0,0,0,0

%N A simple 4-diagonal matrix.

%C Row sums are A113127. Diagonal sums are A109613. Diagonals are A000027.

%F Number triangle where column k has g.f. (1+x+x^2+x^3)(k+1)x^k.

%e Triangle begins

%e 1;

%e 1,2;

%e 1,2,3;

%e 1,2,3,4;

%e 0,2,3,4,5;

%e 0,0,3,4,5,6;

%e 0,0,0,4,5,6,7;

%e 0,0,0,0,5,6,7,8;

%e 0,0,0,0,0,6,7,8,9;

%Y Cf. A113125.

%K easy,nonn,tabl

%O 0,3

%A _Paul Barry_, Oct 14 2005