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A047469 Numbers that are congruent to {0, 1, 2} mod 8. 2
0, 1, 2, 8, 9, 10, 16, 17, 18, 24, 25, 26, 32, 33, 34, 40, 41, 42, 48, 49, 50, 56, 57, 58, 64, 65, 66, 72, 73, 74, 80, 81, 82, 88, 89, 90, 96, 97, 98, 104, 105, 106, 112, 113, 114, 120, 121, 122, 128, 129, 130, 136, 137, 138, 144, 145, 146, 152, 153, 154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..60.

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

FORMULA

G.f.: x*(1 + x + 6*x^2)/((1 - x)*(1 - x^3)).

a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k) = 8*3^(k-1) for k>0. - Philippe Deléham, Oct 24 2011

From Wesley Ivan Hurt, Jun 09 2016: (Start)

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

a(n) = (24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-6, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

a(n) = n + 5*floor((n-1)/3) - 1. - Bruno Berselli, Feb 06 2017

MAPLE

A047469:=n->(24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047469(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{0, 1, 2}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

PROG

(PARI) a(n)=n+(n-1)\3*5-1

(MAGMA) [n : n in [0..150] | n mod 8 in [0..2]]; // Wesley Ivan Hurt, Jun 09 2016

CROSSREFS

Cf. A030341.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

Sequence in context: A050569 A318175 A318182 * A283774 A037456 A277857

Adjacent sequences:  A047466 A047467 A047468 * A047470 A047471 A047472

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)