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URL: https://oeis.org/A321622

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A321622
The Riordan square of the Fine numbers, triangle read by rows, T(n, k) for 0 <= k<= n.
1
1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 6, 10, 7, 3, 1, 1, 18, 31, 19, 10, 4, 1, 1, 57, 97, 61, 29, 13, 5, 1, 1, 186, 316, 196, 96, 40, 16, 6, 1, 1, 622, 1054, 652, 316, 136, 52, 19, 7, 1, 1, 2120, 3586, 2210, 1072, 458, 181, 65, 22, 8, 1, 1
OFFSET
0,11
COMMENTS
Fine numbers as defined in A000957 have a(0) = 0 whereas our variant has a(0) = 1. The rows sums of the triangle are |A002420|.
EXAMPLE
[0] [ 1]
[1] [ 1, 1]
[2] [ 0, 1, 1]
[3] [ 1, 1, 1, 1]
[4] [ 2, 4, 2, 1, 1]
[5] [ 6, 10, 7, 3, 1, 1]
[6] [ 18, 31, 19, 10, 4, 1, 1]
[7] [ 57, 97, 61, 29, 13, 5, 1, 1]
[8] [ 186, 316, 196, 96, 40, 16, 6, 1, 1]
[9] [ 622, 1054, 652, 316, 136, 52, 19, 7, 1, 1]
MAPLE
# The function RiordanSquare is defined in A321620.
Fine := 1 + (1 - sqrt(1 - 4*x))/(3 - sqrt(1 - 4*x)); RiordanSquare(Fine, 10);
MATHEMATICA
(* The function RiordanSquare is defined in A321620. *)
FineGF = 1 + (1 - Sqrt[1 - 4x])/(3 - Sqrt[1 - 4x]);
RiordanSquare[FineGF, 10] (* Jean-François Alcover, Jun 15 2019, from Maple *)
PROG
(SageMath) # uses[riordan_square from A321620]
riordan_square(1 + (1 - sqrt(1 - 4*x))/(3 - sqrt(1 - 4*x)), 10)
CROSSREFS
T(n, 0) = A000957 (Fine), |A002420| (row sums), A000007 (alternating row sums).
Cf. A321620.
Sequence in context: A256156 A342060 A302828 * A087266 A160801 A177002
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 22 2018
STATUS
approved