A047408 -id:A047408 - cp's OEIS frontend

A047622 Numbers that are congruent to {0, 3, 5} mod 8.

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

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A008576, A047408.

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

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

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 *)

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

A047480 Numbers that are congruent to {2, 5, 7} mod 8.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..3000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Different from A038127.

Cf. A047408.

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

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

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 *)

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

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A047622 Numbers that are congruent to {0, 3, 5} mod 8.

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