A178630 a(n) = 18*((10^n - 1)/9)^2.

18, 2178, 221778, 22217778, 2222177778, 222221777778, 22222217777778, 2222222177777778, 222222221777777778, 22222222217777777778, 2222222222177777777778, 222222222221777777777778, 22222222222217777777777778, 2222222222222177777777777778, 222222222222221777777777777778

Offset: 1

Author

Reinhard Zumkeller, May 31 2010

Keywords

• nonn
• easy

Examples

			n=1: ..................... 18 = 9 * 2;
n=2: ................... 2178 = 99 * 22;
n=3: ................. 221778 = 999 * 222;
n=4: ............... 22217778 = 9999 * 2222;
n=5: ............. 2222177778 = 99999 * 22222;
n=6: ........... 222221777778 = 999999 * 222222;
n=7: ......... 22222217777778 = 9999999 * 2222222;
n=8: ....... 2222222177777778 = 99999999 * 22222222;
n=9: ..... 222222221777777778 = 999999999 * 222222222.
		

Links

• G. C. Greubel, 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, A178631, A178632, A178633, A178634, A178635.

Cf. A002276, A002281, A002283, A002477.

Programs

GAP

List([1..20], n -> 18*((10^n-1)/9)^2); # G. C. Greubel, Jan 28 2019

Magma

[18*((10^n - 1)/9)^2: n in [1..20]]; // Vincenzo Librandi, Dec 28 2010

Mathematica

Table[18*((10^n-1)/9)^2, {n, 1, 20}] (* G. C. Greubel, Jan 28 2019 *)

PARI

a(n)=18*(10^n\9)^2 \\ Charles R Greathouse IV, Aug 21 2011

Sage

[18*((10^n-1)/9)^2 for n in (1..20)] # G. C. Greubel, Jan 28 2019

Formula

a(n) = 18*A002477(n) = A002283(n)*A002276(n).

a(n)=((A002276(n-1)*10 + 1)*10^(n-1) + A002281(n-1))*10 + 8.

G.f.: 18*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Ilya Gutkovskiy, Feb 24 2017

From Elmo R. Oliveira, Jul 30 2025: (Start)

E.g.f.: 2*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)