

A104586


Pentagonal wave sequence triangle.


2



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
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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



