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A033118 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,0. 5
1, 8, 65, 520, 4161, 33288, 266305, 2130440, 17043521, 136348168, 1090785345, 8726282760, 69810262081, 558482096648, 4467856773185, 35742854185480, 285942833483841, 2287542667870728, 18300341342965825, 146402730743726600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A015565. - 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 (8,1,-8).

FORMULA

a(n) = 8*a(n-1) + a(n-2) - 8*a(n-3).

a(n) = 2^(3*n+3)/63 - 1/14 - (-1)^n/18. - R. J. Mathar, Jan 08 2011

From Paul Barry, Apr 04 2008: (Start)

G.f. x/((1-x^2)*(1-8*x));

a(n) = (1/3)*Sum_{k=0..n} A001045(3k). (End)

a(n) = floor(8^(n+1)/9)/7 = floor((8*8^n-1)/63) = round((8*8^n-8)/63) = round((16*8^n-9)/63) = ceiling((8*8^n-8)/63). a(n) = a(n-2) + 8^(n-1), n > 2. - Mircea Merca, Dec 28 2010

MAPLE

seq(1/7*floor(8^(n+1)/9), n=1..22); # Mircea Merca, Dec 27 2010

PROG

(MAGMA) [Round((8*8^n-8)/63): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011

CROSSREFS

Pairwise sums are (8^n - 1)/7 (A023001).

Sequence in context: A009373 A293802 A288788 * A033126 A022039 A041025

Adjacent sequences:  A033115 A033116 A033117 * A033119 A033120 A033121

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.