A047408 -id:A047408

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A047622

Numbers that are congruent to {0, 3, 5} mod 8.

+0
6

0, 3, 5, 8, 11, 13, 16, 19, 21, 24, 27, 29, 32, 35, 37, 40, 43, 45, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 99, 101, 104, 107, 109, 112, 115, 117, 120, 123, 125, 128, 131, 133, 136, 139, 141, 144, 147, 149, 152, 155, 157

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

From R. J. Mathar, Oct 18 2008: (Start)

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

a(n) = A008576(n-1), for n>1. (End)

a(n) = floor((8n-7)/3). - Gary Detlefs, Mar 07 2010

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-24-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

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

a(n) = A047408(n) - 1. - Lorenzo Sauras Altuzarra, Jan 31 2023

E.g.f.: 3 + (8/3)*exp(x)*(x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Mar 30 2023

MAPLE

seq(floor((8*n-7)/3), n=1..52); # Gary Detlefs, Mar 07 2010

MATHEMATICA

Select[Range[0, 150], MemberQ[{0, 3, 5}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 04 2012 *)

LinearRecurrence[{1, 0, 1, -1}, {0, 3, 5, 8}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5]]; // Wesley Ivan Hurt, Jun 13 2016

CROSSREFS

Cf. A008576, A047408.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A047480

Numbers that are congruent to {2, 5, 7} mod 8.

+0
3

2, 5, 7, 10, 13, 15, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 45, 47, 50, 53, 55, 58, 61, 63, 66, 69, 71, 74, 77, 79, 82, 85, 87, 90, 93, 95, 98, 101, 103, 106, 109, 111, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 141, 143, 146, 149, 151, 154, 157, 159

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..3000

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

FORMULA

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

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-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.

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

a(n) = A047408(n) + 1. - Lorenzo Sauras Altuzarra, Jan 31 2023

MAPLE

A047480:=n->(24*n-6-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047480(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

MATHEMATICA

Select[Range[0, 150], MemberQ[{2, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Flatten[Table[8 n + {2, 5, 7}, {n, 0, 150}]] (* Vincenzo Librandi, Jun 12 2016 *)

LinearRecurrence[{1, 0, 1, -1}, {2, 5, 7, 10}, 100] (* Harvey P. Dale, Jun 18 2018 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [2, 5, 7]]; // Wesley Ivan Hurt, Jun 10 2016