OFFSET
1,2
COMMENTS
Used in a proof that the initial terms of A309151 are correct.
The S(n) sequence is 1, 7, 11, 77, 111, 777, 1111, 7777, 11111, 77777, ...
LINKS
Robert Israel, Table of n, a(n) for n = 1..1999
R. Israel, Re: Help with a(n) and a cumulative sum, Seqfan (Jul 15 2019).
Index entries for linear recurrences with constant coefficients, signature (-1,10,10).
FORMULA
For even n >= 2, a(n) = 6666...66 (with n/2 6's). For odd n >= 5, a(n) = 3333...334 (with (n-3)/2 3's and a single 4).
From Robert Israel, Jul 15 2019: (Start)
G.f. (1+7*x)/((1+x)*(1-10*x^2)).
a(n) = -a(n - 1) + 10*a(n - 2) + 10*a(n - 3). (End)
a(-n) = a(n+1). - Paul Curtz, Jul 18 2019
a(n) = (1/60)*(-40*(-1)^n + (1 + (-1)^n)*(2^(2+n/2)*5^(1+n/2)) + (1 + (-1)^(n+1))*10^((1+n)/2)). - Stefano Spezia, Jul 20 2019
MAPLE
1, seq(op([6*(10^i-1)/9, 3*(10^i-1)/9+1]), i=1..30); # Robert Israel, Jul 15 2019
MATHEMATICA
CoefficientList[Series[(1 + 7 x)/((1 + x) (1 - 10 x^2)), {x, 0, 26}], x] (* Michael De Vlieger, Jul 18 2019 *)
LinearRecurrence[{-1, 10, 10}, {1, 6, 4}, 30] (* Harvey P. Dale, Jan 02 2022 *)
PROG
(PARI) Vec((1+7*x)/((1+x)*(1-10*x^2)) + O(x^20)) \\ Felix Fröhlich, Jul 15 2019
(PARI) a(n) = if(n==1, 1, if(n%2==0, 6*(10^(n/2)-1)/9, 3*(10^((n-1)/2)-1)/9+1)) \\ Felix Fröhlich, Jul 15 2019
(Magma) I:=[1, 6, 4]; [n le 3 select I[n] else - Self(n-1) + 10*Self(n-2) + 10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Ul 20 2019
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Jul 15 2019
STATUS
approved