|
%I #9 Jun 25 2020 19:28:53
%S 9,292,22922,2229222,222292222,22222922222,2222229222222,
%T 222222292222222,22222222922222222,2222222229222222222,
%U 222222222292222222222,22222222222922222222222,2222222222229222222222222,222222222222292222222222222,22222222222222922222222222222,2222222222222229222222222222222
%N a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F a(n) = 2*A138148(n) + 9*10^n = A002276(2n+1) + 7*10^n.
%F G.f.: (9 - 707*x + 500*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332129 := n -> 2*(10^(2*n+1)-1)/9+7*10^n;
%t Array[2 (10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]
%t LinearRecurrence[{111,-1110,1000},{9,292,22922},20] (* _Harvey P. Dale_, Jun 25 2020 *)
%o (PARI) apply( {A332129(n)=10^(n*2+1)\9*2+7*10^n}, [0..15])
%o (Python) def A332129(n): return 10**(n*2+1)//9*2+7*10**n
%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002276 (2*R_n), A011557 (10^n).
%Y Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y Cf. A332119 .. A332189 (variants with different repeated digit 1, ..., 8).
%Y Cf. A332120 .. A332128 (variants with different middle digit 0, ..., 8).
%K nonn,base,easy
%O 0,1
%A _M. F. Hasler_, Feb 09 2020
| 