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A033117 Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,0. 5
1, 7, 50, 350, 2451, 17157, 120100, 840700, 5884901, 41194307, 288360150, 2018521050, 14129647351, 98907531457, 692352720200, 4846469041400, 33925283289801, 237476983028607, 1662338881200250, 11636372168401750, 81454605178812251, 570182236251685757, 3991275653761800300 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)