A280569 a(n) = (-1)^n * 2 if n = 5*k and n!=0, otherwise a(n) = (-1)^n.

1, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1, -2, 1, -1, 1, -1, 2, -1, 1, -1, 1

Offset: 0

Author

Michael Somos, Jan 05 2017

Keywords

• sign

Examples

			G.f. = 1 - x + x^2 - x^3 + x^4 - 2*x^5 + x^6 - x^7 + x^8 - x^9 + 2*x^10 + ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,-1).

Crossrefs

Cf. A280560.

Programs

Magma

m:=75; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x+x^2)*(1-x^3)/(1+x^5))); // G. C. Greubel, Jul 29 2018

Mathematica

a[ n_] := (-1)^n If[ n != 0 && Divisible[n, 5], 2, 1];
LinearRecurrence[{0,0,0,0,-1},{1,-1,1,-1,1,-2},120] (* or *) PadRight[ {1},120,{2,-1,1,-1,1,-2,1,-1,1,-1}] (* Harvey P. Dale, Jul 18 2021 *)

PARI

{a(n) = (-1)^n * if(n && n%5==0, 2, 1)};

PARI

{a(n) = n=abs(n); polcoeff( (1 - x + x^2) * (1 - x^3) / (1 + x^5) + x * O(x^n), n)};

Formula

Euler transform of length 10 sequence [-1, 1, 0, 0, -1, -1, 0, 0, 0, 1].

a(n) = -b(n) where b() is multiplicative with b(2^e) = -1 if e>0, b(5^e) = 2 if e>0, b(p^e) = 1 otherwise.

G.f.: (1 - x + x^2) * (1 - x^3) / (1 + x^5).

G.f.: 1 - x / (1 + x) - x^5 / (1 + x^5).

a(n) = a(-n) for all n in Z.

a(5*n) = A280560(n) for all n in Z.