A247364 Riordan array (f(x), (f(x)-1)/f(x)) where f(x) = (1 + x - sqrt(1 - 2x - 3x^2))/(2*x).

1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 4, 3, 1, 1, 9, 9, 6, 4, 1, 1, 21, 21, 15, 8, 5, 1, 1, 51, 51, 36, 22, 10, 6, 1, 1, 127, 127, 91, 54, 30, 12, 7, 1, 1, 323, 323, 232, 142, 75, 39, 14, 8, 1, 1, 835, 835, 603, 370, 205, 99, 49, 16, 9, 1, 1, 2188, 2188, 1585, 983

Offset

0,7

Comments

This is essentially the reversal of the triangle in A034928, and A204849 with a duplicated first column.

Row sums are A005554(n+1).

Links

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Formula

T(n,0) = A086246(n+1), T(n+1,1) = A001006(n), T(n+2,2) = A005043(n+2).

Example

Triangle begins:
1
1, 1
1, 1, 1
2, 2, 1, 1
4, 4, 3, 1, 1
9, 9, 6, 4, 1, 1
21, 21, 15, 8, 5, 1, 1
51, 51, 36, 22, 10, 6, 1, 1
Production matrix begins:
1, 1
0, 0, 1
1, 1, 0, 1
1, 1, 1, 0, 1
1, 1, 1, 1, 0, 1
1, 1, 1, 1, 1, 0, 1
1, 1, 1, 1, 1, 1, 0, 1

Prog

(Haskell)
a247364 n k = a247364_tabl !! n !! k
a247364_row n = a247364_tabl !! n
a247364_tabl = [1] : (map reverse a034928_tabf)
-- Reinhard Zumkeller, Sep 20 2014

Crossrefs

Cf. A001006, A005043, A005554, A034928, A086246.

Sequence in context: A331409 A108017 A293208 * A301895 A229054 A133135

Adjacent sequences: A247361 A247362 A247363 * A247365 A247366 A247367

Keyword

nonn,tabl

Author

Philippe Deléham, Sep 14 2014

Status

approved