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A169592
Expansion of 1/((1-x)*(1-x^2-x^4)) + x/(1-3*x^3).
1
1, 2, 2, 2, 7, 4, 7, 16, 12, 12, 47, 20, 33, 114, 54, 54, 331, 88, 143, 872, 232, 232, 2563, 376, 609, 7170, 986, 986, 21279, 1596, 2583, 61632, 4180, 4180, 183911, 6764, 10945, 542386, 17710, 17710, 1622979, 28656, 46367, 4829336, 75024, 75024, 14470299, 121392
OFFSET
0,2
LINKS
Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 303.
FORMULA
G.f.: (1+x+x^4-x^5+x^6-x^2-4*x^3)/((1-x)*(1-3*x^3)*(1-x^2-x^4)).
a(n) = +a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) +3*a(n-6) -3*a(n-7) 3*a(n-8).
a(n) = A103609(n+6) - 1 + 3^((n-1)/3) if n == 1 mod 3.
a(n) = A103609(n+6) - 1 if n == 0 or 2 mod 3.
MATHEMATICA
p[t_]= 1/((1-t)*(1-t^2-t^4)) + t/(1-3*t^3);
CoefficientList[ Series[p[t], {t, 0, 60}], t]
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 60);
Coefficients(R!( 1/((1-x)*(1-x^2-x^4)) +x/(1-3*x^3) )); // G. C. Greubel, Oct 23 2024
(SageMath)
def A169592_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x)*(1-x^2-x^4)) +x/(1-3*x^3) ).list()
A169592_list(60) # G. C. Greubel, Oct 23 2024
CROSSREFS
Cf. A103609.
Sequence in context: A029610 A279967 A094246 * A245600 A266689 A265988
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Dec 02 2009
EXTENSIONS
Notation adapted to OEIS standards, sequence extended, formulas added by the Assoc. Editors of the OEIS [Dec 05 2009]
STATUS
approved