OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (111, -1110, 1000).
FORMULA
a(1)=27, a(2)=3267, a(3)=332667; for n>3, a(n)=111*a(n-1)-1110*a(n-2)+1000*a(n-3). - Harvey P. Dale, Oct 11 2012
G.f.: 27*x*(1 + 10*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Ilya Gutkovskiy, Feb 24 2017
EXAMPLE
n=1: ..................... 27 = 9 * 3;
n=2: ................... 3267 = 99 * 33;
n=3: ................. 332667 = 999 * 333;
n=4: ............... 33326667 = 9999 * 3333;
n=5: ............. 3333266667 = 99999 * 33333;
n=6: ........... 333332666667 = 999999 * 333333;
n=7: ......... 33333326666667 = 9999999 * 3333333;
n=8: ....... 3333333266666667 = 99999999 * 33333333;
n=9: ..... 333333332666666667 = 999999999 * 333333333.
MATHEMATICA
27*(FromDigits/@Table[PadRight[{}, n, 1], {n, 20}])^2 (* or *) LinearRecurrence[ {111, -1110, 1000}, {27, 3267, 332667}, 20] (* Harvey P. Dale, Oct 11 2012 *)
PROG
(Magma) [27*((10^n-1)/9)^2: n in [1..50]]; // Vincenzo Librandi, Dec 28 2010
(Maxima) A178631(n):=27*((10^n-1)/9)^2$ makelist(A178631(n), n, 1, 10); /* Martin Ettl, Nov 12 2012 */
(PARI) a(n)=27*(10^n\9)^2 \\ Charles R Greathouse IV, Jul 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 31 2010
STATUS
approved