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A097122 Expansion of (1-x)^2/((1-x)^3-3x^3). 1
1, 1, 1, 4, 13, 31, 70, 169, 421, 1036, 2521, 6139, 14998, 36661, 89545, 218644, 533941, 1304071, 3184966, 7778449, 18996733, 46394716, 113307745, 276726019, 675833686, 1650553981, 4031064961, 9844867684, 24043624093, 58720529071 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (3,-3,4).

FORMULA

G.f.: (1-2x+x^2)/(1-3x+3x^2-4x^3); a(n)=3a(n-1)-3a(n-2)+4a(n-3); a(n)=sum{k=0..floor(n/3), binomial(n, 3k)3^k }.

MATHEMATICA

CoefficientList[Series[(1-x)^2/((1-x)^3-3x^3), {x, 0, 40}], x]

CROSSREFS

Cf. A024493, A052101.

Sequence in context: A216563 A011937 A307304 * A116411 A333047 A106337

Adjacent sequences:  A097119 A097120 A097121 * A097123 A097124 A097125

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 25 2004

STATUS

approved

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)