A047466 Numbers that are congruent to {0, 1, 2, 4} mod 8.

0, 1, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 24, 25, 26, 28, 32, 33, 34, 36, 40, 41, 42, 44, 48, 49, 50, 52, 56, 57, 58, 60, 64, 65, 66, 68, 72, 73, 74, 76, 80, 81, 82, 84, 88, 89, 90, 92, 96, 97, 98, 100, 104, 105, 106, 108, 112, 113, 114, 116, 120, 121, 122

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Essentially the same as A003485.

Cf. A047461, A047467.

Programs

Magma

[n: n in [0..120] | n mod 8 in [0,1,2,4]];

Maple

A047466:=n->2*n-4+(3-I^(2*n))*(1-I^(n*(n+1)))/4: seq(A047466(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0,120], MemberQ[{0, 1, 2, 4}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 4, 8}, 60] (* Bruno Berselli, Jul 18 2012 *)

Maxima

makelist(2*n-4+(3-(-1)^n)*(1-%i^(n*(n+1)))/4,n,1,60);

PARI

concat(0, Vec((1+x+2*x^2+4*x^3)/((1+x)*(1+x^2)*(1-x)^2)+O(x^60))) (End)

Formula

G.f.: x^2*(1+x+2*x^2+4*x^3) / ( (1+x)*(1+x^2)*(1-x)^2 ). - R. J. Mathar, Oct 08 2011

a(n) = 2*n-4+(3-(-1)^n)*(1-i^(n*(n+1)))/4, where i=sqrt(-1). - Bruno Berselli, Jul 18 2012

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

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

a(2k) = A047461(k), a(2k-1) = A047467(k). (End)

Sum_{n>=2} (-1)^n/a(n) = (1+2*sqrt(2))*Pi/32 + (3+sqrt(2))*log(2)/16 - sqrt(2)*log(2-sqrt(2))/8. - Amiram Eldar, Dec 20 2021