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A257844
a(n) = floor(n/4) * (n mod 4).
9
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.
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, May 10 2015
STATUS
approved