A344420 -id:A344420 - cp's OEIS frontend

A343609 a(n) = floor(n/9).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10

Offset: 0

M. F. Hasler, May 19 2021

Also: Nonnegative integers repeated 9 times (with natural offset 0).

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

Cf. A004526 ([n/2]), A002264 ([n/3]), A002265 ([n/4]), A002266 ([n/5]), A152467 ([n/6]), A132270 ([(n-1)/7]), A132292 ([(n-1)/8]), A059995 ([n/10]), A344420 ([n/11]), A342696 ([n/12]).

Repunits A002275 = A343609 o A011557.

A343609 := n -> iquo(n,9); # illustration: map( A343609, [$0..99] );

A343609[n_] := Floor[n/9]
a[n_] := Quotient[n, 9]; Array[a, 100, 0] (* Amiram Eldar, May 19 2021 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,1,-1},{0,0,0,0,0,0,0,0,0,1},100] (* Harvey P. Dale, Mar 01 2025 *)

PARI
```
apply( A343609(n)=n\9, [0..99])
```

a(n) = A002264(A002264(n)).
a(n) = a(n-1) + a(n-9) - a(n-10), n > 9;
G.f.: x^9/(1 - x - x^9 + x^10).

A342696 a(n) = floor(n/12).

Original entry on oeis.org

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

Offset: 0

Wesley Ivan Hurt, May 18 2021

Agrees with A064459 for n < 144, but a(144) = 12 whereas A064459(144) = 13.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A064459, A221912 (partial sums), A344420 (floor n/11).

Mathematica
```
Floor[Range[0, 200]/12]
```

G.f.: x^12 / ( (1+x)*(1+x^2)*(x^4-x^2+1)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 08 2021

a(n) = a(n-1) + a(n-12) - a(n-13). - Wesley Ivan Hurt, Oct 29 2022

cp's OEIS Frontend

A343609 a(n) = floor(n/9).

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