A117378 Expansion of (1-4*x)/(1-x+x^2).

1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3, -4, -1, 3, 4, 1, -3

Offset

0,2

Comments

Row sums of number triangle A117377.

Period 6: repeat [1, -3, -4, -1, 3, 4]. - Philippe Deléham, Nov 03 2008

Links

Table of n, a(n) for n=0..73.

Tanya Khovanova, Recursive Sequences

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

Formula

G.f.: (1-4*x)/(1-x+x^2).

a(n) = Sum_{k=0..n} (-1)^(n-k) * ( C(k,n-k) + 4*C(k,n-k-1) ).

a(n) = a(n-1) - a(n-2) for n>1. [Philippe Deléham, Nov 03 2008]

a(n) = (1+(-n mod 3))^(n mod 3)*(-1)^floor((n+2)/3). - Wesley Ivan Hurt, Aug 31 2014

a(n) = (3*cos(n*Pi/3) - 7*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 23 2016

E.g.f.: (3*cos(sqrt(3)*x/2) - 7*sqrt(3)*sin(sqrt(3)*x/2))*exp(x/2)/3. - Ilya Gutkovskiy, Jun 27 2016

Maple

A117378:=n->(1+(-n mod 3))^(n mod 3)*(-1)^floor((n+2)/3): seq(A117378(n), n=0..100); # Wesley Ivan Hurt, Aug 31 2014

Mathematica

CoefficientList[Series[(1 - 4 x)/(1 - x + x^2), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
LinearRecurrence[{1, -1}, {1, -3}, 100] (* Harvey P. Dale, Sep 27 2018 *)

Prog

(Magma) [(1+(-n mod 3))^(n mod 3)*(-1)^Floor((n+2)/3) : n in [0..100]]; // Wesley Ivan Hurt, Aug 31 2014

Crossrefs

Cf. A117377.

Sequence in context: A281098 A090279 A101667 * A278518 A088197 A350605

Adjacent sequences: A117375 A117376 A117377 * A117379 A117380 A117381

Keyword

easy,sign

Author

Paul Barry, Mar 10 2006

Status

approved