A257848 a(n) = floor(n/8) * (n mod 8).

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

Offset: 0

Author

M. F. Hasler, May 10 2015

Keywords

• nonn
• base
• easy

Comments

Equivalently, write n in base 8, multiply the last digit by the number with its last digit removed.

Links

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

Crossrefs

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

Programs

Mathematica

Table[Floor[n/8]Mod[n,8],{n,0,90}] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,-1},{0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7},90] (* Harvey P. Dale, Nov 05 2023 *)

PARI

a(n,b=8)=(n=divrem(n,b))[1]*n[2]

PARI

concat([0,0,0,0,0,0,0,0,0], Vec(x^9*(7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2*(x^4+1)^2) + O(x^100))) \\ Colin Barker, May 11 2015

Python

def A257848(n): return (n>>3)*(n&7) # Chai Wah Wu, Jan 19 2023

Formula

a(n) = 2*a(n-8)-a(n-16). - Colin Barker, May 11 2015

G.f.: x^9*(7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2*(x^4+1)^2). - Colin Barker, May 11 2015