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A195938 n/2 if n mod 4 = 2 or 0 otherwise. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

If  S(j,n)= sum(k^j,k=1..n) then, for any odd j, S(j,n) mod n = a(n). [From Gary Detlefs, Oct 26 2011]

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

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).

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^(2*j-1), k=1..n) 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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Sequence in context: A293381 A118112 A245552 * A184762 A330734 A081805

Adjacent sequences:  A195935 A195936 A195937 * A195939 A195940 A195941

KEYWORD

nonn,easy

AUTHOR

Gary Detlefs, Oct 26 2011

STATUS

approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)