A164358 Expansion of (1 - x^2)^2 * (1 - x^3) / ((1 - x)^3 * (1 - x^4)) in powers of x.

1, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2

Offset

0,2

Comments

Coordination sequence for a chain of hexagons joined by single edges. - N. J. A. Sloane, Nov 21 2019

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for coordination sequences

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

Formula

a(n) = 3*b(n) unless n=0 where b(n) is multiplicative with b(2) = 4/3, b(2^e) = 2/3 if e>1, b(p^e) = 1 if p>2.

Euler transform of length 4 sequence [3, -2, -1, 1].

Moebius transform is length 4 sequence [3, 1, 0, -2].

a(n) = a(-n) for all n in Z. a(n+4) = a(n) unless n=0 or n=-4. a(4*n) == 2 unless n=0. a(2*n + 1) = 3. a(4*n + 2) = 4.

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

G.f.: (1+x)*(1+x+x^2)/((1-x)*(1+x^2)). - N. J. A. Sloane, Nov 21 2019

Example

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

Mathematica

a[ n_] := - Boole[n == 0] + 3 - If[ EvenQ[n], (-1)^(n/2), 0];
CoefficientList[Series[(1+3*x+4*x^2+3*x^3+x^4)/(1-x^4), {x, 0, 150}], x] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) {a(n) = -(n==0) + 3 - if( n%2 == 0, (-1)^(n/2), 0)};
(PARI) x='x+O('x^150); Vec((1+3*x+4*x^2+3*x^3+x^4)/(1-x^4)) \\ G. C. Greubel, Sep 26 2018
(Magma) m:=150; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x+4*x^2+3*x^3+x^4)/(1-x^4))); // G. C. Greubel, Sep 26 2018

Crossrefs

Sequence in context: A258451 A332412 A333229 * A275638 A281975 A133617

Adjacent sequences: A164355 A164356 A164357 * A164359 A164360 A164361

Keyword

nonn,easy

Author

Michael Somos, Aug 13 2009

Status

approved