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A117378 Expansion of (1-4*x)/(1-x+x^2). 6
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 (list; graph; refs; listen; history; text; internal format)
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) = (1/6)*{3*(n mod 6)-[(n+1) mod 6)]-4*[(n+2) mod 6)]-3*[(n+3) mod 6)]+[(n+4) mod 6)]+4*[(n+5) mod 6)]}. - Paolo P. Lava, Feb 01 2008

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 *)

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 A087517

Adjacent sequences:  A117375 A117376 A117377 * A117379 A117380 A117381

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 10 2006

STATUS

approved

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Last modified August 20 17:26 EDT 2017. Contains 290837 sequences.