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A020699
Expansion of (1-3*x)/(1-5*x).
9
1, 2, 10, 50, 250, 1250, 6250, 31250, 156250, 781250, 3906250, 19531250, 97656250, 488281250, 2441406250, 12207031250, 61035156250, 305175781250, 1525878906250, 7629394531250, 38146972656250, 190734863281250, 953674316406250
OFFSET
0,2
COMMENTS
Partial sums are A034478.
Except for the first two terms 1 and 2, these are the integers that satisfy phi(n) = 2*n/5. - Michel Marcus, Jul 14 2015
For n>=1, period of powers of 4 mod 10^n. See A000302. - Martin Renner, Jun 12 2020
LINKS
D Bevan, D Levin, P Nugent, J Pantone, L Pudwell, Pattern avoidance in forests of binary shrubs, arXiv preprint arXiv:1510:08036 [math.CO], 2015-2016.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1037 (archived version of page)
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
FORMULA
a(n) = 2*5^(n-1) for n>0.
E.g.f.: (2*exp(5*x)+3)/5; a(n)=(2*5^n+3*0^n)/5. - Paul Barry, Sep 03 2003
a(n) = sum{k=0..n, C(n-1, k)*(Jac(2n-2k)+Jac(2n-2k-1))}+0^n/2, where Jac(n)=A001045(n). - Paul Barry, Jun 07 2005
a(0)=1, a(1)=2, a(n) = 5*a(n-1) for n>=2. [Vincenzo Librandi, Jan 01 2011]
a(n) = A020729(n-1), n>0. - R. J. Mathar, Sep 16 2016
MAPLE
seq(`if`(n=0, 1, 2*5^(n-1)), n=0..22); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
CoefficientList[Series[(1 - 3 x)/(1 - 5 x), {x, 0, 22}], x] (* Michael De Vlieger, Jul 14 2015 *)
PROG
(PARI) Vec((1-3*x)/(1-5*x) + O(x^30)) \\ Michel Marcus, Jul 14 2015
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved