A108286 Triangle read by rows; columns are simple recursive sequences.

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..45.

Formula

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.

Example

First few rows of the triangle are:
1;
3, 1;
6, 4, 1;
10, 11; 5, 1;
15, 26, 18, 6, 1;
21, 57, 58, 27, 7, 1;
...
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.

Crossrefs

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

Sequence in context: A104712 A122177 A255874 * A185944 A131415 A210230

Adjacent sequences: A108283 A108284 A108285 * A108287 A108288 A108289

Keyword

nonn,tabl

Author

Gary W. Adamson, May 31 2005

Status

approved