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A376081
Irregular triangle read by rows: row n is the periodic part of the Leonardo numbers (A001595) modulo n.
3
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
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
KEYWORD
nonn,tabf
AUTHOR
Paolo Xausa, Sep 09 2024
STATUS
approved