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A047529 Numbers that are congruent to {1, 3, 7} mod 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

Sequence in context: A027897 A027892 A158938 * A125667 A072939 A171947

Adjacent sequences:  A047526 A047527 A047528 * A047530 A047531 A047532

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 8 04:31 EST 2019. Contains 329850 sequences. (Running on oeis4.)