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A029739 Numbers that are congruent to {1, 3, 4} mod 6. 3
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 (list; graph; refs; listen; history; text; internal format)
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

a(n) = -2 + Sum_{k=1..n} ((k mod 3) + ((k+1) mod 3)), with n >= 1. - Paolo P. Lava, Sep 03 2010

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

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Last modified October 2 08:07 EDT 2022. Contains 357191 sequences. (Running on oeis4.)