A178632 a(n) = 45*((10^n - 1)/9)^2.

45, 5445, 554445, 55544445, 5555444445, 555554444445, 55555544444445, 5555555444444445, 555555554444444445, 55555555544444444445, 5555555555444444444445, 555555555554444444444445, 55555555555544444444444445, 5555555555555444444444444445, 555555555555554444444444444445

Offset: 1

Author

Reinhard Zumkeller, May 31 2010

Keywords

• nonn
• easy

Examples

			n=1: ..................... 45 = 9 * 5;
n=2: ................... 5445 = 99 * 55;
n=3: ................. 554445 = 999 * 555;
n=4: ............... 55544445 = 9999 * 5555;
n=5: ............. 5555444445 = 99999 * 55555;
n=6: ........... 555554444445 = 999999 * 555555;
n=7: ......... 55555544444445 = 9999999 * 5555555;
n=8: ....... 5555555444444445 = 99999999 * 55555555;
n=9: ..... 555555554444444445 = 999999999 * 555555555.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. A059988, A075412, A075415, A178630, A178631, A178633, A178634, A178635.

Cf. A002278, A002279, A002283, A002477.

Programs

Magma

[45*((10^n-1)/9)^2: n in [1..50]]; // Vincenzo Librandi, Dec 28 2010

Mathematica

45 (FromDigits/@Table[PadRight[{}, n, 1], {n, 20}])^2 (* Vincenzo Librandi, Mar 20 2014 *)
LinearRecurrence[{111,-1110,1000},{45,5445,554445},20] (* Harvey P. Dale, Jan 23 2019 *)

Maxima

A178632(n):=45*((10^n-1)/9)^2$ makelist(A178632(n),n,1,12); /* Martin Ettl, Nov 08 2012 */

PARI

a(n)=45*(10^n\9)^2 \\ Charles R Greathouse IV, Jul 02 2013

Formula

a(n) = 45*A002477(n) = A002283(n)*A002279(n).

a(n) = (A002279(n-1)*10^n + A002278(n))*10 + 5.

G.f.: 45*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Ilya Gutkovskiy, Feb 24 2017

From Elmo R. Oliveira, Aug 01 2025: (Start)

E.g.f.: 5*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9.

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 3. (End)