A257849 a(n) = floor(n/9) * (n mod 9).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 2, 4, 6, 8, 10, 12, 14, 16, 0, 3, 6, 9, 12, 15, 18, 21, 24, 0, 4, 8, 12, 16, 20, 24, 28, 32, 0, 5, 10, 15, 20, 25, 30, 35, 40, 0, 6, 12, 18, 24, 30, 36, 42, 48, 0, 7, 14, 21, 28, 35, 42, 49, 56, 0, 8, 16, 24, 32, 40, 48, 56, 64, 0

Offset: 0

Author

M. F. Hasler, May 10 2015

Keywords

• nonn
• base
• easy

Comments

Equivalently, write n in base 9, multiply the last digit by the number with its last digit removed.

See A142150(n-1) for the base 2 analog, and A115273, A257844 - A257850 for the base 3 - base 10 variants.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A142150 (the base 2 analog), A115273, A257844 - A257850.

Programs

Magma

[Floor(n/9)*(n mod 9): n in [0..100]]; // Vincenzo Librandi, May 11 2015

Mathematica

Table[Floor[n/9] Mod[n, 9], {n, 100}] (* Vincenzo Librandi, May 11 2015 *)

PARI

A257849(n)=n\9*(n%9)

PARI

concat([0,0,0,0,0,0,0,0,0,0], Vec(x^10*(8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2*(x^6+x^3+1)^2) + O(x^100))) \\ Colin Barker, May 11 2015

Python

from math import prod
def A257849(n): return prod(divmod(n,9)) # Chai Wah Wu, Jan 19 2023

Sage

[floor(n/9)*(n % 9)  for n in (0..80)]; # Bruno Berselli, May 11 2015

Formula

a(n) = 2*a(n-9)-a(n-18). - Colin Barker, May 11 2015

G.f.: x^10*(8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2*(x^6+x^3+1)^2). - Colin Barker, May 11 2015