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A047523 Numbers that are congruent to {0, 1, 7} mod 8. 3
0, 1, 7, 8, 9, 15, 16, 17, 23, 24, 25, 31, 32, 33, 39, 40, 41, 47, 48, 49, 55, 56, 57, 63, 64, 65, 71, 72, 73, 79, 80, 81, 87, 88, 89, 95, 96, 97, 103, 104, 105, 111, 112, 113, 119, 120, 121, 127, 128, 129, 135, 136, 137, 143, 144, 145, 151, 152, 153, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

G.f.: x^2*(1+6*x+x^2)  / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 13 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = (24*n-24+15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*Pi*n/3))/9.

a(3k) = 8k-1, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

MAPLE

A047523:=n->(24*n-24+15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*Pi*n/3))/9: seq(A047523(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{0, 1, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)

LinearRecurrence[{1, 0, 1, -1}, {0, 1, 7, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 1, 7]]; // Wesley Ivan Hurt, Jun 13 2016

CROSSREFS

Sequence in context: A037369 A076599 A067197 * A108177 A165480 A285468

Adjacent sequences:  A047520 A047521 A047522 * A047524 A047525 A047526

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)