A104891 a(0) = 0; a(n) = 5*a(n-1) + 5.

0, 5, 30, 155, 780, 3905, 19530, 97655, 488280, 2441405, 12207030, 61035155, 305175780, 1525878905, 7629394530, 38146972655, 190734863280, 953674316405, 4768371582030, 23841857910155, 119209289550780, 596046447753905, 2980232238769530, 14901161193847655

Offset: 0

Author

Alexandre Wajnberg, Apr 24 2005

Keywords

• easy
• nonn

Comments

Number of integers from 0 to (10^n)-1 that lack 0, 1, 2, 3 and 4 as a digit.

Number of monic irreducible polynomials of degree 1 in GF(5)[x1,...,xn]. - Max Alekseyev, Jan 23 2006

Examples

			a(3) = 5*a(2) + 5 = 5*30 + 5 = 155.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A000225, A000918, A029858, A052379, A052386, A080674.

Row n=5 of A228275.

Programs

Magma

[5*(5^n -1)/4: n in [0..30]]; // G. C. Greubel, Jun 15 2021

Maple

a:=n->add(5^j,j=1..n): seq(a(n),n=0..30); # Zerinvary Lajos, Jun 27 2007

Mathematica

RecurrenceTable[{a[n]==5*a[n-1]+5, a[0]==0}, a, {n, 0, 30}] (* Vaclav Kotesovec, Jul 25 2014 *)
NestList[5#+5&,0,30] (* Harvey P. Dale, Oct 04 2019 *)

PARI

concat(0, Vec(5*x/((x-1)*(5*x-1)) + O(x^30))) \\ Colin Barker, Jul 25 2014

Sage

[5*(5^n -1)/4 for n in (0..30)] # G. C. Greubel, Jun 15 2021

Formula

a(n) = 5*(5^n - 1)/4. - Max Alekseyev, Jan 23 2006

a(n) = a(n-1) + 5^n with a(0)=0. - Vincenzo Librandi, Nov 13 2010

From Colin Barker, Jul 25 2014: (Start)

a(n) = 6*a(n-1) - 5*a(n-2).

G.f.: 5*x / ((1-x)*(1-5*x)). (End)

E.g.f.: (5/4)*(exp(5*x) - exp(x)). - G. C. Greubel, Jun 15 2021