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A342149 Infinite square matrix A(m,n) = F(m+1) mod (n+1), m,n >= 1, where F = Fibonacci = A000045, read by falling antidiagonals. 2
1, 1, 0, 1, 2, 1, 1, 2, 0, 1, 1, 2, 3, 2, 0, 1, 2, 3, 1, 2, 1, 1, 2, 3, 0, 0, 1, 1, 1, 2, 3, 5, 3, 1, 0, 0, 1, 2, 3, 5, 2, 3, 1, 1, 1, 1, 2, 3, 5, 1, 1, 1, 2, 1, 1, 1, 2, 3, 5, 0, 6, 3, 4, 3, 2, 0, 1, 2, 3, 5, 8, 5, 0, 4, 0, 1, 0, 1, 1, 2, 3, 5, 8, 4, 5, 6, 1, 4, 0, 2, 1, 1, 2, 3, 5, 8, 3, 3, 2, 6, 5, 4, 1, 2, 0, 1, 2, 3, 5, 8, 2, 1, 7, 7, 5, 0, 3, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The determinant of the (upper left) n X n submatrix is zero iff n >= 35. (Observation by Bill Gosper, math-fun mailing list.)

The rows are eventually constant sequences, reaching the limit Fibonacci(m+1) after the final 0 in column n = Fibonacci(m+1); the sequence of columns converges to the Fibonacci sequence A000045 without the initial 0.

LINKS

Table of n, a(n) for n=1..120.

Bill Gosper, mysteriously vanishing sequence, math-fun mailing list, Jul 10 2021

FORMULA

A(m,n) = A342148(m+1,n+1) = A000045(m+1) mod (n+1).

See A342148 for more formulas.

EXAMPLE

The matrix reads:

[1 1 1 1 1 1 1 ...]

[0 2 2 2 2 2 2 ...]

[1 0 3 3 3 3 3 ...]

[1 2 1 0 5 5 5 ...]

[0 2 0 3 2 1 0 ...]

[1 1 1 3 1 6 5 ...]

[1 0 1 1 3 0 5 ...]

(...)

PROG

(PARI) A342149(m, n)=fibonacci(m+1)%(n+1)

row(n)=[A342149(m, n-m+1) | m<-[1..n]] \\ The n-th falling antidiagonal.

concat([ row(n) | n <- [1..10] ]) \\ (beginning of) the "flattened" sequence.

CROSSREFS

Cf. A000045, A342148 (matrix extended by an additional initial row and column).

Sequence in context: A157188 A329257 A173266 * A224326 A096496 A117209

Adjacent sequences: A342146 A342147 A342148 * A342150 A342151 A342152

KEYWORD

nonn,tabl

AUTHOR

M. F. Hasler, Jul 12 2021

STATUS

approved

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Last modified January 27 11:39 EST 2023. Contains 359839 sequences. (Running on oeis4.)