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A075415
Squares of A002280 or numbers (666...6)^2.
27
0, 36, 4356, 443556, 44435556, 4444355556, 444443555556, 44444435555556, 4444444355555556, 444444443555555556, 44444444435555555556, 4444444444355555555556, 444444444443555555555556, 44444444444435555555555556, 4444444444444355555555555556
OFFSET
0,2
COMMENTS
A transformation of the Wonderful Demlo numbers (A002477).
FORMULA
a(n) = A002280(n)^2 = (6 * A002275(n))^2 = 36 * (A002275(n))^2.
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)
a(n) = ((A002278(n-1)*10+3)*10^(n-1)+A002279(n-1))*10+6 for n>0.
a(n) = A002283(n)*A002278(n). (End)
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 *)
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