OFFSET
0,2
COMMENTS
A transformation of the Wonderful Demlo numbers (A002477).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
G. Villemin, Variations sur les carrés
Index entries for linear recurrences with constant coefficients, signature (11, -10).
FORMULA
a(n) = {111111... (2n times)} - 2*{ 111... (n times)} a(n) = A000042(2n) - 2*A000042(n). - Amarnath Murthy, Jul 21 2003
a(n) = {333... (n times)}^2 ={111...(n times)}{000... (n times)} - {111... (n times)}. For example, 333^2 = 111000 - 111 = 110889. - Kyle D. Balliet, Mar 07 2009
a(n) = (10^(n+1)-10)^2/900. - José de Jesús Camacho Medina, Apr 01 2016
EXAMPLE
a(2) = 33^2 = 1089.
Contribution from Reinhard Zumkeller, May 31 2010: (Start)
n=1: ...................... 9 = 9 * 1;
n=2: ................... 1089 = 99 * 11;
n=3: ................. 110889 = 999 * 111;
n=4: ............... 11108889 = 9999 * 1111;
n=5: ............. 1111088889 = 99999 * 11111;
n=6: ........... 111110888889 = 999999 * 111111;
n=7: ......... 11111108888889 = 9999999 * 1111111;
n=8: ....... 1111111088888889 = 99999999 * 11111111;
n=9: ..... 111111110888888889 = 999999999 * 111111111. (End)
MATHEMATICA
LinearRecurrence[{11, -10}, {0, 3}, 20]^2 (* Vincenzo Librandi, Mar 20 2014 *)
Table[FromDigits[PadRight[{}, n, 9]]FromDigits[PadRight[{}, n, 1]], {n, 0, 15}] (* Harvey P. Dale, Feb 12 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002
STATUS
approved