A047620 Numbers that are congruent to {0, 1, 2, 5} mod 8.

0, 1, 2, 5, 8, 9, 10, 13, 16, 17, 18, 21, 24, 25, 26, 29, 32, 33, 34, 37, 40, 41, 42, 45, 48, 49, 50, 53, 56, 57, 58, 61, 64, 65, 66, 69, 72, 73, 74, 77, 80, 81, 82, 85, 88, 89, 90, 93, 96, 97, 98, 101, 104, 105, 106, 109, 112, 113, 114, 117, 120, 121, 122

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Crossrefs

Cf. A016813, A047404, A047431, A047467, A047546, A047557, A047578, A056594.

Programs

Magma

[n : n in [0..150] | n mod 8 in [0, 1, 2, 5]]; // Wesley Ivan Hurt, May 22 2016

Maple

A047620:=n->(4*n-6+I^(1-n)-I^(1+n))/2: seq(A047620(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Table[(4n-6+I^(1-n)-I^(1+n))/2, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{2,-2,2,-1},{0,1,2,5},120] (* Harvey P. Dale, Mar 11 2017 *)

Sage

[lucas_number1(n,0,1)+2*n-3 for n in range(1,57)] # Zerinvary Lajos, Jul 06 2008

Formula

From R. J. Mathar, Oct 08 2011: (Start)

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

a(n) = 2*n-3+sin(n*Pi/2). (End)

From Wesley Ivan Hurt, May 22 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(n) = (4n-6+I^(1-n)-I^(1+n))/2 where i=sqrt(-1).

a(2n+2) = A016813(n) n>0, a(2n-1) = A047467(n). (End)

Sum_{n>=2} (-1)^n/a(n) = Pi/16 + 5*log(2)/8. - Amiram Eldar, Dec 19 2021

Extensions

More terms from Wesley Ivan Hurt, May 22 2016