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

Author

Nick Hobson, Jun 27 2010

Keywords

• easy
• nonn

Examples

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

Programs

Magma

&cat [[1,1,1,2*n]: n in [1..30]]; // Vincenzo Librandi, Dec 05 2016

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 *)

PARI

s=0; for(n=1, 100, s+=n^3; print(s%(n+2)))

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

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