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

0,12

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).

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

Mathematica

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

Prog

(PARI) A257849(n)=n\9*(n%9)
(Magma) [Floor(n/9)*(n mod 9): n in [0..100]]; // Vincenzo Librandi, May 11 2015
(Sage) [floor(n/9)*(n % 9)  for n in (0..80)]; # Bruno Berselli, May 11 2015
(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

Crossrefs

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

Sequence in context: A010878 A309788 A326746 * A190727 A195832 A265523

Adjacent sequences: A257846 A257847 A257848 * A257850 A257851 A257852

Keyword

nonn,base,easy

Author

M. F. Hasler, May 10 2015

Status

approved