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

1,3

Links

Table of n, a(n) for n=1..63.

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

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

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 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n-3 for n in range(1, 57)] # Zerinvary Lajos, Jul 06 2008
(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 5]]; // Wesley Ivan Hurt, May 22 2016

Crossrefs

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

Sequence in context: A085254 A274035 A068537 * A283205 A322916 A062803

Adjacent sequences: A047617 A047618 A047619 * A047621 A047622 A047623

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 22 2016

Status

approved