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

1,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A015552.

Sequence in context: A278875 A266360 A288787 * A096882 A033125 A022037

Adjacent sequences: A033114 A033115 A033116 * A033118 A033119 A033120

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved