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

Author

M. F. Hasler, May 19 2021

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

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.

Programs

Maple

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

Mathematica

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])

Formula

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).