A376081 - OEIS

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A376081

Irregular triangle read by rows: row n is the periodic part of the Leonardo numbers (A001595) modulo n.

0, 1, 1, 1, 0, 2, 0, 0, 1, 2, 1, 1, 3, 1, 1, 3, 0, 4, 0, 0, 1, 2, 4, 2, 2, 0, 3, 4, 3, 3, 2, 1, 4, 1, 1, 3, 5, 3, 3, 1, 5, 1, 1, 3, 5, 2, 1, 4, 6, 4, 4, 2, 0, 3, 4, 1, 6, 1, 1, 3, 5, 1, 7, 1, 1, 3, 5, 0, 6, 7, 5, 4, 1, 6, 8, 6, 6, 4, 2, 7, 1, 0, 2, 3, 6, 1, 8

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

OFFSET

1,6

COMMENTS

Each row n >= 3 ends in (1, n-1) (see Wikipedia article).

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..12347 (rows 1..150 of triangle, flattened).

Wikipedia, Leonardo number.

FORMULA

T(n,k) = A001595(k) mod n, with 0 <= k < A376082(n).

EXAMPLE

Triangle begins:

[1] 0;

[2] 1;

[3] 1, 1, 0, 2, 0, 0, 1, 2;

[4] 1, 1, 3;

[5] 1, 1, 3, 0, 4, 0, 0, 1, 2, 4, 2, 2, 0, 3, 4, 3, 3, 2, 1, 4;

[6] 1, 1, 3, 5, 3, 3, 1, 5;

[7] 1, 1, 3, 5, 2, 1, 4, 6, 4, 4, 2, 0, 3, 4, 1, 6;

[8] 1, 1, 3, 5, 1, 7;

[9] 1, 1, 3, 5, 0, 6, 7, 5, 4, 1, 6, 8, 6, 6, 4, 2, 7, 1, 0, 2, 3, 6, 1, 8;

...

For n = 8:

A001595 = 1, 1, 3, 5, 9, 15, 25, 41, 67, 109, 177, 287, 465, ...

A001595 mod 8 = 1, 1, 3, 5, 1, 7, 1, 1, 3, 5, 1, 7, 1, ...

\_______________/

periodic part

MATHEMATICA

A376081row[n_] := If[n < 3, {n - 1}, Module[{k = 1}, NestWhileList[Mod[2 * Fibonacci[++k] - 1, n] &, 1, {#, #2} != {1, n-1} &, {3, 2}]]];

Array[A376081row, 10]

CROSSREFS

Cf. A001595, A161553, A376082 (row lengths), A376083 (row sums).

Sequence in context: A372809 A210255 A283319 * A049321 A204425 A245187

Adjacent sequences: A376078 A376079 A376080 * A376082 A376083 A376084

KEYWORD

nonn,tabf

AUTHOR

Paolo Xausa, Sep 09 2024

STATUS

approved