A047624 Numbers that are congruent to {0, 1, 3, 5} mod 8.

0, 1, 3, 5, 8, 9, 11, 13, 16, 17, 19, 21, 24, 25, 27, 29, 32, 33, 35, 37, 40, 41, 43, 45, 48, 49, 51, 53, 56, 57, 59, 61, 64, 65, 67, 69, 72, 73, 75, 77, 80, 81, 83, 85, 88, 89, 91, 93, 96, 97, 99, 101, 104, 105, 107, 109, 112, 113, 115, 117, 120, 121, 123

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From Reinhard Zumkeller, Feb 21 2010: (Start)

a(n+1) = A173562(n) - A173562(n-1);

a(n+1) - a(n) = A140081(n-1) + 1;

a(n) = A140201(n-1) + A042948(A004526(n-1)). (End)

G.f.: x^2*(1+2*x+2*x^2+3*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 01 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-11-i^(2*n)+i^(1-n)-i^(1+n))/4 where i=sqrt(-1).

a(2k) = A016813(k-1) for k>0, a(2k-1) = A047470(k). (End)

E.g.f.: (6 + sin(x) + (4*x - 5)*sinh(x) + (4*x - 6)*cosh(x))/2. - Ilya Gutkovskiy, Jun 01 2016

Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(2))*Pi/16 + (8-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8. - Amiram Eldar, Dec 20 2021

Maple

A047624:=n->(8*n-11-I^(2*n)+I^(1-n)-I^(1+n))/4: seq(A047624(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Table[(8n-11-I^(2n)+I^(1-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, Jun 01 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 3, 5, 8}, 100] (* G. C. Greubel, Jun 01 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 5]]; // Wesley Ivan Hurt, Jun 01 2016

Crossrefs

Cf. A004526, A016813, A042948, A047470, A140081, A140201, A173562.

Sequence in context: A085722 A023980 A189029 * A108594 A325425 A286048

Adjacent sequences: A047621 A047622 A047623 * A047625 A047626 A047627

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved