A033117 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

1, 7, 50, 350, 2451, 17157, 120100, 840700, 5884901, 41194307, 288360150, 2018521050, 14129647351, 98907531457, 692352720200, 4846469041400, 33925283289801, 237476983028607, 1662338881200250, 11636372168401750, 81454605178812251, 570182236251685757, 3991275653761800300

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Partial sums of round(7^n/8), A015552. - Mircea Merca, Dec 28 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,1,-7).

Crossrefs

Cf. A015552.

Programs

Magma

[Floor((7*7^n-1)/48): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011

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

Maple

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

Mathematica

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 *)
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 *)
CoefficientList[Series[1/((1 - x) (1 - 7 x) (1 + x)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)

Formula

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

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

a(n) = (7*7^n - 4 - 3*(-1)^n)/48. - Bruno Berselli, Jan 19 2011

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