A162507 Triangle read by rows, finite differences of an array generated by an infinite product (Cf. A162506).

1, 2, 1, 2, 3, 1, 4, 3, 4, 1, 4, 9, 4, 5, 1, 6, 12, 12, 5, 6, 1, 6, 18, 24, 15, 6, 7, 1, 8, 24, 36, 30, 18, 7, 8, 1, 8, 33, 60, 60, 36, 21, 8, 9, 1, 10, 39, 88, 95, 72, 42, 24, 9, 10, 1, 10, 51, 124, 160, 138, 84, 48, 27, 10, 11

Offset

2,2

Comments

Row sums = A162506 starting (1, 3, 6, 12, 23, 42, 77,...).

Links

Table of n, a(n) for n=2..66.

Formula

Given the infinite product and array shown in A162506, we have

a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...];

The array is a, a*b, a*b*c,... Finite differences of array columns = rows of the triangle, deleting the first "1".

Example

The array =
1,...1,...1,...1,...1,...; = a
1,...1,...3,...3,...5,...; = a*b
1,...1,...3,...6,...8,...; = a*b*c
1,...1,...3,...6,..12,...; = a*b*c*d
...
taking finite differences from the top, then discarding the first "1",
we obtain triangle A162507:
1;
1, 2;
1, 2, 3;
1, 4, 3, 4;
1, 4, 9, 4, 5;
1, 6, 12, 12, 5, 6;
1, 6, 18, 24, 15, 6, 7;
1, 8, 24, 36, 30, 18, 7, 8;
1, 8, 33, 60, 60, 36, 21, 8, 9;
1, 10, 39, 88, 95, 72, 42, 24, 9, 10;
1, 10, 51, 124, 160, 138, 84, 48, 27, 10, 11;
...

Crossrefs

Cf. A162506.

Sequence in context: A217762 A172467 A110582 * A091298 A306641 A055884

Adjacent sequences: A162504 A162505 A162506 * A162508 A162509 A162510

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 04 2009

Status

approved