A033117 - OEIS

%I #40 Sep 08 2022 08:44:51

%S 1,7,50,350,2451,17157,120100,840700,5884901,41194307,288360150,

%T 2018521050,14129647351,98907531457,692352720200,4846469041400,

%U 33925283289801,237476983028607,1662338881200250,11636372168401750,81454605178812251,570182236251685757,3991275653761800300

%N Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

%C Partial sums of round(7^n/8), A015552. - _Mircea Merca_, Dec 28 2010

%H Vincenzo Librandi, <a href="/A033117/b033117.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,1,-7).

%F G.f.: x / ((1-x)*(1-7*x)*(1+x)).

%F a(n) = 7*a(n-1) + a(n-2) - 7*a(n-3).

%F a(n) = (7*7^n - 4 - 3*(-1)^n)/48. - _Bruno Berselli_, Jan 19 2011

%F a(n) = (1/6)*floor(7^(n+1)/8) = floor((7*7^n-1)/48) = ceiling((7*7^n-7)/48) = round((7*7^n-7)/48) = round((7*7^n-4)/48); a(n) = a(n-2) + 7^(n-1), n > 2. - _Mircea Merca_, Dec 28 2010

%p A033117 := proc(n) add( round(7^i/8),i=0..n) ; end proc:

%t Join[{a=1,b=7},Table[c=6*b+7*a+1;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 06 2011 *)

%t Module[{nn=30,c},c=PadRight[{},nn,{1,0}];Table[FromDigits[Take[c,n],7],{n,nn}]] (* or *) LinearRecurrence[{7,1,-7},{1,7,50},30] (* _Harvey P. Dale_, Feb 13 2014 *)

%t CoefficientList[Series[1/((1 - x) (1 - 7 x) (1 + x)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 26 2014 *)

%o (Magma) [Floor((7*7^n-1)/48): n in [1..30]]; // _Vincenzo Librandi_, Jun 25 2011

%o (Magma) I:=[1, 7, 50]; [n le 3 select I[n] else 7*Self(n-1)+Self(n-2)-7*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Mar 26 2014

%Y Cf. A015552.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_