OFFSET
0,2
COMMENTS
A transformation of the Wonderful Demlo numbers (A002477).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
G. Villemin, Variations sur les carrés
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).
FORMULA
a(n) = (6*(10^n-1)/9)^2 = (4/9)*(10^(2*n) - 2*10^n + 1), which is n-1 4's, followed by a 3, n-1 5's and a 6. - Ignacio Larrosa Cañestro, Feb 26 2005
From Reinhard Zumkeller, May 31 2010: (Start)
G.f.: 36*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Arkadiusz Wesolowski, Dec 26 2011
EXAMPLE
a(2) = 66^2 = 4356.
From Reinhard Zumkeller, May 31 2010: (Start)
n=1: ..................... 36 = 9 * 4;
n=2: ................... 4356 = 99 * 44;
n=3: ................. 443556 = 999 * 444;
n=4: ............... 44435556 = 9999 * 4444;
n=5: ............. 4444355556 = 99999 * 44444;
n=6: ........... 444443555556 = 999999 * 444444;
n=7: ......... 44444435555556 = 9999999 * 4444444;
n=8: ....... 4444444355555556 = 99999999 * 44444444;
n=9: ..... 444444443555555556 = 999999999 * 444444444. (End)
MATHEMATICA
Table[FromDigits[PadRight[{}, n, 6]]^2, {n, 0, 20}] (* or *) LinearRecurrence[ {111, -1110, 1000}, {0, 36, 4356}, 20] (* Harvey P. Dale, May 20 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Taylor (michael.taylor(AT)vf.vodafone.co.uk), Sep 14 2002
EXTENSIONS
Edited by Alois P. Heinz, Aug 21 2019 (merged with A102794, submitted by Richard C. Schroeppel, Feb 26 2005)
STATUS
approved