A016134 Expansion of g.f. 1/((1-2*x)*(1-10*x)).

1, 12, 124, 1248, 12496, 124992, 1249984, 12499968, 124999936, 1249999872, 12499999744, 124999999488, 1249999998976, 12499999997952, 124999999995904, 1249999999991808, 12499999999983616, 124999999999967232, 1249999999999934464, 12499999999999868928, 124999999999999737856

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			G.f. = 1 + 12*x + 124*x^2 + 1248*x^3 + 12496*x^4 + 124992*x^5 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (12,-20).

Crossrefs

Cf. A060458. - Zerinvary Lajos, Jun 05 2009

Cf. A000079, A011557.

Programs

Magma

[2^n*(5^(n+1)-1)/4: n in [0..20]]; // Vincenzo Librandi, Oct 09 2011

Mathematica

f[n_] := Sum[2^(k - 1)*10^(n - k), {k, n}]; Array[f, 18] (* Robert G. Wilson v, Dec 03 2016 *)
a[ n_] := (5 * 10^n - 2^n) / 4; (* Michael Somos, Dec 03 2016 *)
LinearRecurrence[{12,-20},{1,12},20] (* Harvey P. Dale, Jul 28 2020 *)

PARI

Vec(1/((1-2*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Sage

[lucas_number1(n,12,20) for n in range(1, 18)] # Zerinvary Lajos, Apr 27 2009

Sage

[(10^n - 2^n)/8 for n in range(1,19)] # Zerinvary Lajos, Jun 05 2009

Formula

a(n) = 125*10^(n-2) - 2^(n-2) = a(n-1)*10 + 2^n. - Henry Bottomley, Jun 06 2000

G.f.: 1/(1-12*x+20*x^2). - Zerinvary Lajos, Apr 27 2009 [corrected by R. J. Mathar, Mar 14 2011]

From Michael Somos, Dec 03 2016: (Start)

Convolution of A000079 and A011557.

a(n) = (5*10^n - 2^n)/4. (End)

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(2*x)*(5*exp(8*x) - 1)/4.

a(n) = A060458(n+1)/8.

a(n) = 12*a(n-1) - 20*a(n-2). (End)