|
Search: id:A104586
|
|
|
| A104586 |
|
Pentagonal wave sequence triangle. |
|
+0
3
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Row sums = A086500: 1, 9, 18, 50, 75, 147, 196...
|
|
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: A147677 A090243 A145338 this_sequence A040048 A070429 A050092
Adjacent sequences: A104583 A104584 A104585 this_sequence A104587 A104588 A104589
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 17 2005
|
|
|
Search completed in 0.002 seconds
|
