A195938 a(n) = n/2 if n mod 4 = 2, 0 otherwise.

0, 1, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 7, 0, 0, 0, 9, 0, 0, 0, 11, 0, 0, 0, 13, 0, 0, 0, 15, 0, 0, 0, 17, 0, 0, 0, 19, 0, 0, 0, 21, 0, 0, 0, 23, 0, 0, 0, 25, 0, 0, 0, 27, 0, 0, 0, 29, 0, 0, 0, 31, 0, 0, 0, 33, 0, 0, 0, 35, 0, 0, 0, 37, 0, 0, 0, 39

Offset: 1

Author

Gary Detlefs, Oct 26 2011

Keywords

• nonn
• easy

Comments

If S(j,n) = Sum_{k=1..n} k^j then, for any odd j, S(j,n) mod n = a(n). - Gary Detlefs, Oct 26 2011

Odd numbers A005408, with 3 zeros between them. - T. D. Noe, Oct 27 2011

Examples

			G.f. = x + 3*x^5 + 5*x^9 + 7*x^13 + 9*x^17 + 11*x^21 + 13*x^25 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

Programs

Maple

S:=(j,n)-> sum(k^j,k=1..n):seq(S(3,n) mod n, n=1..70);

Mathematica

a[n_] := If[Mod[n, 4] == 2, n/2, 0]; Table[a[n], {n, 80}] (* Alonso del Arte, Oct 26 2011 *)

PARI

a(n)=if(n%4==2,n/2) \\ Charles R Greathouse IV, Oct 26 2011

Formula

Euler transform of length 8 sequence [ 0, 0, 0, 3, 0, 0, 0, -1]. - Michael Somos, Oct 29 2011

a(n) = -a(-n) for all n in Z. - Michael Somos, Oct 29 2011

a(n) = (Sum_{k=1..n} k^(2*j-1)) mod n, for any j.

a(n) = (n/2)*floor((1/2)*cos((n+2)*Pi/2) + 1/2).

G.f.: (1+x^4)*x^2/(1-x^4)^2. - Philippe Deléham, Oct 27 2011

a(n) = binomial(n^2,3)/4 mod n. - Gary Detlefs, May 04 2013

a(n) = n*(1 - i^n)*(1 + i^(2*n))/8, where i=sqrt(-1). - Ammar Khatab, Aug 25 2020