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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)