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
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, May 10 2015
STATUS
approved