A178205 - OEIS

%I #31 Sep 08 2022 08:45:53

%S 1,1,1,11,21,31,141,351,661,2071,5581,12191,32901,88711,210621,539631,

%T 1426741,3532951,8929261,23196671,58526181,147818791,379785501,

%U 965047311,2443235221,6241090231,15891563341,40323915551,102734817861

%N a(n) = a(n-1) + 10*a(n-3) for n > 2; a(0) = a(1) = a(2) = 1.

%C If x=a(n), y=a(n+1), z=a(n+2), then 100*x^3 + 10*x^2*z - 30*x*y*z + 10*x*y^2 + 10*y^3 - 2*y*z^2 + y^2*z + z^3 = 10^(n+2), for n >= 0. - _Alexander Samokrutov_, Jul 03 2015

%H G. C. Greubel, <a href="/A178205/b178205.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,10).

%F G.f.: 1/(1-x-10*x^3).

%t RecurrenceTable[{a[n] == a[n - 1] + 10 a[n - 3], a[0] == a[1] == a[2] == 1}, a, {n, 0, 28}] (* or *)

%t CoefficientList[Series[1/(1 - x - 10 x^3), {x, 0, 28}], x] (* _Michael De Vlieger_, Jul 09 2015 *)

%t LinearRecurrence[{1, 0, 10}, {1, 1, 1}, 30] (* _Vincenzo Librandi_, Jul 19 2015 *)

%o (PARI) {m=29; v=concat([1, 1, 1], vector(m-3)); for(n=4, m, v[n]=v[n-1]+10*v[n-3]); v}

%o (Magma) I:=[1,1,1]; [n le 3 select I[n] else Self(n-1) + 10*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jul 19 2015

%o (PARI) x='x+O('x^50); Vec(1/(1-x-10*x^3)) \\ _G. C. Greubel_, Apr 29 2017

%Y Cf. A000930 (a(n)=a(n-1)+a(n-3), a(0)=a(1)=a(2)=1).

%K nonn,easy

%O 0,4

%A _Mark Dols_, May 22 2010

%E Edited and extended by _Klaus Brockhaus_, May 23 2010