A029739 Numbers that are congruent to {1, 3, 4} mod 6.

1, 3, 4, 7, 9, 10, 13, 15, 16, 19, 21, 22, 25, 27, 28, 31, 33, 34, 37, 39, 40, 43, 45, 46, 49, 51, 52, 55, 57, 58, 61, 63, 64, 67, 69, 70, 73, 75, 76, 79, 81, 82, 85, 87, 88, 91, 93, 94, 97, 99, 100, 103, 105, 106, 109, 111, 112, 115, 117, 118, 121, 123, 124

Offset

1,2

Links

Table of n, a(n) for n=1..63.

Patrick De Geest, More palindromic products of integer sequences: Three consecutive palindromes.

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

Formula

G.f.: x*(2*x+1)*(x^2+1)/((1+x+x^2)*(x-1)^2). - R. J. Mathar, Aug 24 2011

From Wesley Ivan Hurt, Jun 11 2016: (Start)

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

a(n) = 2*(3*n - 2 - cos(2*n*Pi/3))/3.

a(3k) = 6k-2, a(3k-1) = 6k-3, a(3k-2) = 6k-5. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = (3+2*sqrt(3))*Pi/36 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/6. - Amiram Eldar, Dec 16 2021

Maple

A029739:=n->2*(3*n-2-cos(2*n*Pi/3))/3: seq(A029739(n), n=1..100); # Wesley Ivan Hurt, Jun 11 2016

Mathematica

Select[Range[0, 202], MemberQ[{1, 3, 4}, Mod[#, 6]] &] (* and *) Join[{1}, Accumulate[Total /@ CellularAutomaton[65, {1, 1, 0, 0, 1, 0}, 100]]] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 4, 7}, 80] (* Harvey P. Dale, Aug 21 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 6 in {1, 3, 4}]; // Vincenzo Librandi, Dec 29 2010

Crossrefs

Sequence in context: A059010 A066928 A032726 * A005098 A185661 A276786

Adjacent sequences: A029736 A029737 A029738 * A029740 A029741 A029742

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved