OFFSET
1,1
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 33 at p. 62.
Walther Lietzmann, Lustiges und Merkwuerdiges von Zahlen und Formen, (F. Hirt, Breslau 1921-43), p. 149.
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).
FORMULA
G.f.: 63*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Ilya Gutkovskiy, Feb 24 2017
E.g.f.: 7*exp(x)*(1 - 2*exp(9*x) + exp(99*x))/9. - Stefano Spezia, Jul 31 2024
EXAMPLE
n=1: ..................... 63 = 9 * 7;
n=2: ................... 7623 = 99 * 77;
n=3: ................. 776223 = 999 * 777;
n=4: ............... 77762223 = 9999 * 7777;
n=5: ............. 7777622223 = 99999 * 77777;
n=6: ........... 777776222223 = 999999 * 777777;
n=7: ......... 77777762222223 = 9999999 * 7777777;
n=8: ....... 7777777622222223 = 99999999 * 77777777;
n=9: ..... 777777776222222223 = 999999999 * 777777777.
MATHEMATICA
63((10^Range[15]-1)/9)^2 (* or *) Table[FromDigits[Join[PadRight[{}, n, 7], {6}, PadRight[{}, n, 2], {3}]], {n, 0, 15}] (* Harvey P. Dale, Apr 23 2012 *)
PROG
(Magma) [63*((10^n - 1)/9)^2: n in [1..20]]; // Vincenzo Librandi, Dec 28 2010
(PARI) a(n)=63*(10^n\9)^2 \\ Charles R Greathouse IV, Jul 02 2013
(Sage) [63*((10^n - 1)/9)^2 for n in (1..20)] # G. C. Greubel, Jan 28 2019
(GAP) List([1..20], n -> 63*((10^n - 1)/9)^2); # G. C. Greubel, Jan 28 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 31 2010
STATUS
approved