A047472 Numbers that are congruent to {0, 1, 3} (mod 8).

0, 1, 3, 8, 9, 11, 16, 17, 19, 24, 25, 27, 32, 33, 35, 40, 41, 43, 48, 49, 51, 56, 57, 59, 64, 65, 67, 72, 73, 75, 80, 81, 83, 88, 89, 91, 96, 97, 99, 104, 105, 107, 112, 113, 115, 120, 121, 123, 128, 129, 131, 136, 137, 139, 144, 145, 147, 152, 153, 155

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

Equals partial sums of (0, 1, 2, 5, 1, 2, 5, 1, 2, 5, ...). - Gary W. Adamson, Jun 19 2008

From Colin Barker, Jan 26 2012: (Start)

G.f.: x^2*(1+2*x+5*x^2)/(1-x-x^3+x^4).

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

From Wesley Ivan Hurt, Jun 09 2016: (Start)

a(n) = 8*n/3 - 4 - cos(2*n*Pi/3) + 5*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3k) = 8k-5, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)

Maple

A047472:=n->8*n/3-4-cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047472(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016

Mathematica

Select[Range[0, 150], MemberQ[{0, 1, 3}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 09 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3]]; // Wesley Ivan Hurt, Jun 09 2016

Crossrefs

Sequence in context: A024550 A173179 A225555 * A304204 A028960 A139491

Adjacent sequences: A047469 A047470 A047471 * A047473 A047474 A047475

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved