A104586 Pentagonal wave sequence triangle.

1, 7, 2, 12, 5, 1, 26, 15, 7, 2, 35, 22, 12, 5, 1, 57, 40, 26, 15, 7, 2, 70, 51, 35, 22, 12, 5, 1, 100, 77, 57, 40, 26, 15, 7, 2

Offset

1,2

Comments

Row sums = A086500: 1, 9, 18, 50, 75, 147, 196...

Links

Table of n, a(n) for n=1..36.

Formula

Odd columns are terms of A104584, pentagonal wave sequence of the first kind, (starting with 1): 1, 7, 12, 26, 35, 57, 70... Even columns are terms of A104585, pentagonal wave sequence of the second kind (starting with 2): 2, 5, 15, 22, 40, 51... Odd rows are pentagonal numbers (A000326) starting with "1" at the right. Even rows are second pentagonal numbers (A005449) starting with 2 at the right. The triangle is extracted from a matrix product A * B, A = [1; 1, 2; 1, 2, 1; 1, 2, 1, 2;...], B = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1;...] (both infinite lower triangular matrices, with the rest zeros).

Example

The first few rows are:
1;
7, 2;
12, 5, 1;
26, 15, 7, 2;
35, 22, 12, 5, 1;
57, 40, 26, 15, 7, 2;
70, 51, 35, 22, 12, 5, 1;
...

Crossrefs

Cf. A086500, A104584, A104585, A000326, A005449, A049452, A033570, A049453, A033568.

Sequence in context: A090243 A216150 A145338 * A323995 A040048 A070429

Adjacent sequences: A104583 A104584 A104585 * A104587 A104588 A104589

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 17 2005

Status

approved