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

0,7

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A267852 A328568 A219864 * A194745 A248342 A002392

Adjacent sequences: A257841 A257842 A257843 * A257845 A257846 A257847

Keyword

nonn,base,easy

Author

M. F. Hasler, May 10 2015

Status

approved