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A097178 Expansion of (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)). 2
1, 10, 100, 1110, 10000, 122110, 1000000, 13333110, 100000000, 1446644110, 10000000000, 156111055110, 1000000000000, 16767216566110, 100000000000000, 1793488873177110, 10000000000000000, 191142376190888110 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Partial sums are A097177.
LINKS
FORMULA
a(n) = (55/sqrt(101))*( (sqrt(101))^n - (-sqrt(101))^n ) + 10^n * (11*(-1)^n-9)/2.
a(n) = 201*a(n-2) - 10100*a(n-4).
MAPLE
seq(coeff(series((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)), x, n+1), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019
MATHEMATICA
CoefficientList[Series[(1+10x-101x^2-900x^3)/((1-100x^2)(1-101x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 13 2017 *)
LinearRecurrence[{0, 201, 0, -10100}, {1, 10, 100, 1110}, 20] (* Harvey P. Dale, Mar 03 2018 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))) \\ G. C. Greubel, Sep 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)) )); // G. C. Greubel, Sep 17 2019
(Sage)
def A097178_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))).list()
A097178_list(20) # G. C. Greubel, Sep 17 2019
(GAP) a:=[1, 10, 100, 1110];; for n in [5..20] do a[n]:=201*a[n-2] - 10100*a[n-4]; od; a; # G. C. Greubel, Sep 17 2019
CROSSREFS
Sequence in context: A164832 A144822 A199763 * A283288 A283377 A283352
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 30 2004
STATUS
approved

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Last modified June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)