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A167373 Expansion of (1+x)*(3*x+1)/(1+x+x^2). 3
1, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Bisection of A138034.
Also row 2n of A137276 or A135929.
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, Chapter 22.
LINKS
FORMULA
G.f.: (1+x)*(3*x+1)/(1+x+x^2).
a(n) = a(n-3), n>4.
a(n) = - a(n-1) - a(n-2) for n>2.
a(n) = 4*sin(2*n*Pi/3)/sqrt(3)-2*cos(2*n*Pi/3) for n>0 with a(0)=1. - Wesley Ivan Hurt, Jun 12 2016
MAPLE
A167373 := proc(n)
option remember;
if n < 4 then
op(n+1, [1, 3, -1, -2]) ;
else
procname(n-3) ;
end if;
end proc:
seq(A167373(n), n=0..20) ; # R. J. Mathar, Feb 06 2020
MATHEMATICA
CoefficientList[Series[(1 + x)*(3*x + 1)/(1 + x + x^2), {x, 0, 50}], x] (* G. C. Greubel, Jun 12 2016 *)
LinearRecurrence[{-1, -1}, {1, 3, -1}, 120] (* Harvey P. Dale, Apr 05 2023 *)
CROSSREFS
Sequence in context: A195588 A153510 A288537 * A079722 A079723 A080511
KEYWORD
sign,easy
AUTHOR
Jamel Ghanouchi, Nov 02 2009
EXTENSIONS
Edited by R. J. Mathar, Nov 03 2009
Further edited and extended by Simon Plouffe, Nov 23 2009
Recomputed by N. J. A. Sloane, Dec 20 2009
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)