A020699 Expansion of (1-3*x)/(1-5*x).

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

Nathaniel Johnston, Table of n, a(n) for n = 0..250

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

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.

Index entries for linear recurrences with constant coefficients, signature (5).

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

Cf. A034478, A001045, A020729, A000302.

Sequence in context: A015945 A015954 A015949 * A020729 A110170 A026332

Adjacent sequences: A020696 A020697 A020698 * A020700 A020701 A020702

Keyword

nonn,easy

Author

David W. Wilson

Status

approved