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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A015945 A015954 A015949 * A020729 A110170 A026332
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)