A047529 Numbers that are congruent to {1, 3, 7} mod 8.

1, 3, 7, 9, 11, 15, 17, 19, 23, 25, 27, 31, 33, 35, 39, 41, 43, 47, 49, 51, 55, 57, 59, 63, 65, 67, 71, 73, 75, 79, 81, 83, 87, 89, 91, 95, 97, 99, 103, 105, 107, 111, 113, 115, 119, 121, 123, 127, 129, 131, 135, 137, 139, 143, 145, 147, 151, 153, 155, 159

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (24*n+2*sqrt(3)*sin(2*Pi*n/3)+6*cos(2*Pi*n/3)-15)/9. - Fred Daniel Kline, Nov 12 2015

From Colin Barker, Nov 12 2015: (Start)

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

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

a(n+3) = a(n) + 8 for all n in Z. - Michael Somos, Nov 15 2015

a(3k) = 8k-1, a(3k-1) = 8k-5, a(3k-2) = 8k-7. - Wesley Ivan Hurt, Jun 13 2016

a(n) = 8 * floor((n-1) / 3) + 2^(((n-1) mod 3) + 1) - 1. - Fred Daniel Kline, Aug 09 2016

a(n) = 2*(n + floor(n/3)) - 1. - Wolfdieter Lang, Sep 10 2021

Example

G.f. = x + 3*x^2 + 7*x^3 + 9*x^4 + 11*x^5 + 15*x^6 + 17*x^7 + 19*x^8 + 23*x^9 + ...

Maple

A047529:=n->(24*n+2*sqrt(3)*sin(2*Pi*n/3)+6*cos(2*Pi*n/3)-15)/9: seq(A047529(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Mathematica

Select[Range[150], MemberQ[{1, 3, 7}, Mod[#, 8]]&] (* Harvey P. Dale, May 02 2011 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 7, 9}, 100] (* Vincenzo Librandi, Jun 14 2016 *)

Prog

(PARI) Vec(x*(x^3+4*x^2+2*x+1)/((x-1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Nov 12 2015
(PARI) {a(n) = n\3 * 8 + [-1, 1, 3][n%3 + 1]}; /* Michael Somos, Nov 15 2015 */
(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 7]]; // Wesley Ivan Hurt, Jun 13 2016

Crossrefs

Cf. A047478, A047484, A047623.

Sequence in context: A027897 A027892 A158938 * A359567 A125667 A072939

Adjacent sequences: A047526 A047527 A047528 * A047530 A047531 A047532

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved