A051109 Expansion of g.f. (1+2*x+5*x^2)/(1-10*x^3).

1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000, 200000, 500000, 1000000, 2000000, 5000000, 10000000, 20000000, 50000000, 100000000, 200000000, 500000000, 1000000000, 2000000000, 5000000000, 10000000000, 20000000000, 50000000000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,10).

Formula

a(3*n) = 10^n, a(3*n+1) = 2*10^n, a(3*n+2) = 5*10^n.

a(n) = ( 1 + (n mod 3)^2 )*10^floor(n/3). - Justin L. Brown (jlbrown(AT)neo.tamu.edu), Jun 17 2004

G.f.: (1+2*x+5*x^2)/(1-10*x^3). - Philippe Deléham, Apr 08 2013

a(n) = 10*a(n-3) with n>2, a(0)=1, a(1)=2, a(2)=5. - Philippe Deléham, Apr 08 2013

From Amiram Eldar, Jul 27 2023: (Start)

Sum_{n>=0} 1/a(n) = 17/9.

Sum_{n>=0} (-1)^n/a(n) = 7/11. (End)

Mathematica

a[n_]:= a[n]= If[n<3, Fibonacci[2n+1], 10*a[n-3]];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jul 23 2023 *)

Prog

(Python) print( [ ((n % 3) ** 2 + 1) * 10**int(n/3) for n in range(100)] )
(Magma) [(1 +(n mod 3)^2)*10^Floor(n/3): n in [0..40]]; // G. C. Greubel, Jul 23 2023
(SageMath) [(1 +(n%3)^2)*10^(n//3) for n in range(41)] # G. C. Greubel, Jul 23 2023

Crossrefs

Cf. A117727.

Sequence in context: A352120 A176692 A212951 * A124146 A262408 A344378

Adjacent sequences: A051106 A051107 A051108 * A051110 A051111 A051112

Keyword

easy,nonn

Author

Robert Lozyniak (11(AT)onna.com)

Extensions

Second formula corrected by Peter C. Lauterbach, Nov 12 2010

New name using g.f. from Joerg Arndt, Jul 23 2023

Status

approved