A257844 a(n) = floor(n/4) * (n mod 4).

0, 0, 0, 0, 0, 1, 2, 3, 0, 2, 4, 6, 0, 3, 6, 9, 0, 4, 8, 12, 0, 5, 10, 15, 0, 6, 12, 18, 0, 7, 14, 21, 0, 8, 16, 24, 0, 9, 18, 27, 0, 10, 20, 30, 0, 11, 22, 33, 0, 12, 24, 36, 0, 13, 26, 39, 0, 14, 28, 42, 0, 15, 30, 45, 0, 16, 32, 48, 0, 17, 34, 51, 0, 18, 36

Offset: 0

Author

M. F. Hasler, May 10 2015

Keywords

• nonn
• base
• easy

Comments

Equivalently, write n in base 4, 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 (0,0,0,2,0,0,0,-1).

Crossrefs

Cf. A142150 (the base-2 analog), A115273, A257845 - A257850.

Programs

Magma

[Floor(n/4)*(n mod 4) : n in [0..100]]; // Wesley Ivan Hurt, Jun 22 2015

Magma

I:=[0,0,0,0,0,1,2,3]; [n le 8 select I[n] else 2*Self(n-4)-Self(n-8): n in [1..100]]; // Vincenzo Librandi, Jun 23 2015

Maple

A257844:=n->floor(n/4)*(n mod 4): seq(A257844(n), n=0..100); # Wesley Ivan Hurt, Jun 22 2015

Mathematica

Table[Floor[n/4] Mod[n, 4], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 22 2015 *)

PARI

a(n,b=4)=(n=divrem(n,b))[1]*n[2]

PARI

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

Python

def A257844(n): return (n>>2)*(n&3) # Chai Wah Wu, Jan 27 2023

Formula

a(n) = 2*a(n-4) - a(n-8), n > 8. - Colin Barker, May 11 2015

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

a(n) = (3 - 2*(-1)^((2*n - 1 + (-1)^n)/4) - (-1)^n)*(2*n - 3 + 2*(-1)^((2*n - 1 + (-1)^n)/4) + (-1)^n)/16. - Wesley Ivan Hurt, Jun 22 2015