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Triangle read by rows; columns are simple recursive sequences.
2

%I #6 Apr 10 2013 13:28:16

%S 1,3,1,6,4,1,10,11,5,1,15,26,18,6,1,21,57,58,27,7,1,28,120,179,112,38,

%T 8,1,36,247,543,453,194,51,9,1,45,502,1636,1818,975,310,66,10,1

%N Triangle read by rows; columns are simple recursive sequences.

%C Left column = triangular numbers; Col. 2, (1, 4, 11...) = A000295; Col. 3, (1, 5, 18...) = A000340; Col. 4, (1, 6, 27...) = A014825; Col.5, (1, 7, 38...) = A014827.

%F r-th term in n-th column: initial "1", then a(r) = n*a(r-1) + r. Diagonals of A108285 become the columns of A108286.

%e First few rows of the triangle are:

%e 1;

%e 3, 1;

%e 6, 4, 1;

%e 10, 11; 5, 1;

%e 15, 26, 18, 6, 1;

%e 21, 57, 58, 27, 7, 1;

%e ...

%e 3rd offset column: (1, 5, 18, 58...) = "1", then a(r) = 3*a(r-1) + r; e.g. 58 = 3*18 + 4 since 58 is the fourth term in the third column.

%Y Cf. A108285, A000295, A000340, A014825, A014827.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, May 31 2005