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A112525
Expansion of 1/(1 - 100*x^2 - 100*x^3).
1
1, 0, 100, 100, 10000, 20000, 1010000, 3000000, 103000000, 401000000, 10600000000, 50400000000, 1100100000000, 6100000000000, 115050000000000, 720010000000000, 12115000000000000, 83506000000000000
OFFSET
0,3
COMMENTS
10^(floor((n+1)/2)) | a(n), n>=0. - G. C. Greubel, Jan 12 2022
FORMULA
a(n) = Sum_{k=0..floor(n/2)} C((n-k)/2, k)*10^(n-k)*(1 + (-1)^(n-k))/2.
MATHEMATICA
a[n_]:= a[n]= (1/2)*Sum[(1+(-1)^(k+n))*10^(n-k)*Binomial[(n-k)/2, k], {k, 0, Floor[n/2]}];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jan 12 2022 *)
CoefficientList[Series[1/(1-100x^2-100x^3), {x, 0, 20}], x] (* or *) LinearRecurrence[ {0, 100, 100}, {1, 0, 100}, 20] (* Harvey P. Dale, Mar 18 2023 *)
PROG
(Sage)
def A112525_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1 -100*x^2 -100*x^3) ).list()
A112525_list(40) # G. C. Greubel, Jan 12 2022
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 40);
Coefficients(R!( 1/(1 -100*x^2 -100*x^3) )); // G. C. Greubel, Jan 12 2022
CROSSREFS
Sequence in context: A308660 A220023 A115048 * A000865 A135600 A134999
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 09 2005
STATUS
approved