A047462 Numbers that are congruent to {0, 1, 4} mod 8.

0, 1, 4, 8, 9, 12, 16, 17, 20, 24, 25, 28, 32, 33, 36, 40, 41, 44, 48, 49, 52, 56, 57, 60, 64, 65, 68, 72, 73, 76, 80, 81, 84, 88, 89, 92, 96, 97, 100, 104, 105, 108, 112, 113, 116, 120, 121, 124, 128, 129, 132, 136, 137, 140, 144, 145, 148, 152, 153, 156

Offset

1,3

Links

Table of n, a(n) for n=1..60.

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

Formula

G.f.: x^2*(1+3*x+4*x^2)/((1-x)^2*(1+x+x^2)). [Colin Barker, May 13 2012]

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-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 8k-4, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

Maple

A047462:=n->(24*n-33-3*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047462(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 4}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 10 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 4]]; // Wesley Ivan Hurt, Jun 10 2016

Crossrefs

Sequence in context: A221865 A004753 A144794 * A020671 A171598 A259241

Adjacent sequences: A047459 A047460 A047461 * A047463 A047464 A047465

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved