A033118 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.

1, 8, 65, 520, 4161, 33288, 266305, 2130440, 17043521, 136348168, 1090785345, 8726282760, 69810262081, 558482096648, 4467856773185, 35742854185480, 285942833483841, 2287542667870728, 18300341342965825, 146402730743726600

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

Mathematica

Table[FromDigits[PadRight[{}, n, {1, 0}], 8], {n, 20}] (* or *) LinearRecurrence[ {8, 1, -8}, {1, 8, 65}, 20] (* Harvey P. Dale, Jan 20 2021 *)

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: A316872 A317600 A288788 * A033126 A022039 A041025

Adjacent sequences: A033115 A033116 A033117 * A033119 A033120 A033121

Keyword

nonn,base,easy

Author

Clark Kimberling

Status

approved