A179054 a(n) = (1^k + 2^k + ... + n^k) modulo (n+2), where k is any odd integer greater than or equal to 3.

1, 1, 1, 4, 1, 1, 1, 6, 1, 1, 1, 8, 1, 1, 1, 10, 1, 1, 1, 12, 1, 1, 1, 14, 1, 1, 1, 16, 1, 1, 1, 18, 1, 1, 1, 20, 1, 1, 1, 22, 1, 1, 1, 24, 1, 1, 1, 26, 1, 1, 1, 28, 1, 1, 1, 30, 1, 1, 1, 32, 1, 1, 1, 34, 1, 1, 1, 36, 1, 1, 1, 38, 1, 1, 1, 40, 1, 1, 1, 42, 1, 1, 1, 44, 1, 1, 1, 46, 1, 1, 1, 48, 1, 1, 1

Offset

1,4

Links

Robert Israel, 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

a(n) = 2m+2, if n = 4m for some integer m; a(n) = 1 otherwise.

G.f.: (x+x^2+x^3+4*x^4-x^5-x^6-x^7-2*x^8)/(1-2*x^4+x^8). - Robert Israel, Dec 05 2016

Example

a(4) = (1^3 + 2^3 + 3^3 + 4^3) mod 6 = 100 mod 6 = 4.

Maple

seq(op([1, 1, 1, 2*k]), k=2..50); # Robert Israel, Dec 05 2016

Mathematica

f[n_] := Mod[n^2(n + 1)^2/4, n + 2]; Array[f, 100] (* Robert G. Wilson v, Jul 01 2010 *)
LinearRecurrence[{0, 0, 0, 2, 0, 0, 0, -1}, {1, 1, 1, 4, 1, 1, 1, 6}, 100] (* Vincenzo Librandi, Dec 05 2016 *)

Prog

(PARI) s=0; for(n=1, 100, s+=n^3; print(s%(n+2)))
(Magma)  &cat [[1, 1, 1, 2*n]: n in [1..30]]; // Vincenzo Librandi, Dec 05 2016

Crossrefs

Sequence in context: A162400 A332012 A365788 * A063928 A344910 A326135

Adjacent sequences: A179051 A179052 A179053 * A179055 A179056 A179057

Keyword

easy,nonn

Author

Nick Hobson, Jun 27 2010

Extensions

Typo in name of sequence corrected and formula added by Nick Hobson, Jun 27 2010

More terms from Robert G. Wilson v, Jul 01 2010

Status

approved