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A047475 Numbers that are congruent to {1, 2, 3} mod 8. 2
1, 2, 3, 9, 10, 11, 17, 18, 19, 25, 26, 27, 33, 34, 35, 41, 42, 43, 49, 50, 51, 57, 58, 59, 65, 66, 67, 73, 74, 75, 81, 82, 83, 89, 90, 91, 97, 98, 99, 105, 106, 107, 113, 114, 115, 121, 122, 123, 129, 130, 131, 137, 138, 139, 145, 146, 147, 153, 154, 155 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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+x^2+5*x^3)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 13 2012]

a(n) = 1+8*floor((n-1)/3)+((n-1) mod 3). - Alois P. Heinz, May 13 2012

From Wesley Ivan Hurt, Jun 10 2016: (Start)

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

a(n) = (24*n-30-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-5, a(3k-1) = 8k-6, a(3k-2) = 8k-7. (End)

MAPLE

A047475:=n->(24*n-30-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047475(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

MATHEMATICA

Flatten[#+{1, 2, 3}&/@(8*Range[0, 20])] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 2, 3, 9}, 70] (* Harvey P. Dale, Nov 06 2013 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1..3]]; // Wesley Ivan Hurt, Jun 10 2016

CROSSREFS

Sequence in context: A309348 A270886 A133557 * A291610 A285428 A039012

Adjacent sequences:  A047472 A047473 A047474 * A047476 A047477 A047478

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 22 13:46 EDT 2021. Contains 345380 sequences. (Running on oeis4.)