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A257179 Expansion of (1 + x^5) / ((1 - x) * (1 + x^4)) in powers of x. 4
1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

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

FORMULA

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

Moebius transform is length 8 sequence [1, 0, 0, -1, 0, 0, 0, 2].

a(n) is multiplicative with a(2) = 1, a(4) = 0, a(2^e) = 2 if e>2, a(p^e) = 1 if p>2 and a(0) = 1.

G.f.: (1 + x^5) / ((1 - x) * (1 + x^4)).

G.f.: (1 - x^4) * (1 - x^10) / ((1 - x) * (1 - x^5) * (1 - x^8)).

G.f.: -1 + 1 / (1 - x) + 1 / (1 + x^4).

a(n) = a(-n) for all n in Z. a(n+8) = a(n) unless n=0 or n=-8. a(8*n) = 2 unless n=0. a(2*n + 1) = a(4*n + 2) = 1. a(8*n + 4) = 0.

a(n) = A259042(n+4) unless n = 0.

EXAMPLE

G.f. = 1 + x + x^2 + x^3 + x^5 + x^6 + x^7 + 2*x^8 + x^9 + x^10 + x^11 + ...

MATHEMATICA

a[ n_] := Boole[n != 0] - Boole[Mod[n, 4] == 0] + 2 Boole[Mod[n, 8] == 0];

a[ n_] := -Boole[n == 0] + {1, 1, 1, 0, 1, 1, 1, 2}[[Mod[n, 8, 1]]];

a[ n_] := SeriesCoefficient[ (1 + x^5) / ((1 - x) * (1 + x^4)), {x, 0, Abs@n}];

PROG

(PARI) {a(n) = (n != 0) - (n%4 == 0) + 2*(n%8 == 0)};

(PARI) {a(n) = -(n==0) + [2, 1, 1, 1, 0, 1, 1, 1][n%8 + 1]};

(PARI) {a(n) = polcoeff( (1 + x^5) / ((1 - x) * (1 + x^4)) + x * O(x^abs(n)), abs(n))};

CROSSREFS

Cf. A010877, A259042.

Sequence in context: A281490 A326695 A323191 * A259042 A333179 A240021

Adjacent sequences:  A257176 A257177 A257178 * A257180 A257181 A257182

KEYWORD

nonn,mult,easy

AUTHOR

Michael Somos, Apr 17 2015

EXTENSIONS

More terms from Antti Karttunen, Jul 29 2018

STATUS

approved

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Last modified May 30 04:38 EDT 2020. Contains 334711 sequences. (Running on oeis4.)