

A047266


Numbers that are congruent to {0, 1, 5} mod 6.


5



0, 1, 5, 6, 7, 11, 12, 13, 17, 18, 19, 23, 24, 25, 29, 30, 31, 35, 36, 37, 41, 42, 43, 47, 48, 49, 53, 54, 55, 59, 60, 61, 65, 66, 67, 71, 72, 73, 77, 78, 79, 83, 84, 85, 89, 90, 91, 95, 96, 97, 101, 102, 103, 107, 108, 109, 113, 114, 115, 119, 120, 121, 125
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OFFSET

1,3


COMMENTS

a(n+3) is the Hankel transform of A005773(n+3).  Paul Barry, Nov 04 2008
The numbers m == 0, 2 or 10 mod 12 (the doubles of this sequence, that is, 10, 12, 14, 22, 24, 26, 34, ...) have the property that exactly 1/4 of the 3part partitions of m form the sides of a triangle. See Stack Exchange, 2013, link.  Ed Pegg Jr, Dec 19 2013
Row sum of a triangle where two rules build the triangle. #1 Start with the value "1" at the top of the triangle. #2 Require every "triple" to contain the values 1,2,3 (see link below). Compare with A136289 that has "3" at the apex.  Craig Knecht, Oct 17 2015
Nonnegative m such that floor(k*m^2/6) = k*floor(m^2/6), where k = 2, 3, 4 or 5. [Bruno Berselli, Dec 03 2015]


LINKS

Table of n, a(n) for n=1..63.
Craig Knecht, Triangular row sum of A204259.
Stack Exchange, Prove: Exactly a quarter of 3part partitions of numbers >2 equal to 0, 2, 10 mod 12 will make a triangle, 2013.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).


FORMULA

G.f.: x^2*(1+4*x+x^2) / ((1+x+x^2)*(x1)^2).  R. J. Mathar, Oct 08 2011
a(n) = 2*(n1) + A057078(n).  Robert Israel, Dec 01 2014
a(n) = a(n1) + a(n3)  a(n4) for n>4.  Wesley Ivan Hurt, Nov 09 2015
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = 2*n2+cos(2*n*Pi/3)+sin(2*n*Pi/3)/sqrt(3).
a(3k) = 6k1, a(3k1) = 6k5, a(3k2) = 6k6. (End)


MAPLE

seq(seq(6*s+j, j=[0, 1, 5]), s=0..100); # Robert Israel, Dec 01 2014


MATHEMATICA

Select[Range[0, 200], Mod[#, 6] == 0  Mod[#, 6] == 1  Mod[#, 6] == 5 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)


PROG

(PARI) concat(0, Vec(x^2*(1+4*x+x^2)/((1+x+x^2)*(x1)^2) + O(x^100))) \\ Altug Alkan, Oct 17 2015
(MAGMA) [n : n in [0..150]  n mod 6 in [0, 1, 5]]; // Wesley Ivan Hurt, Jun 13 2016


CROSSREFS

Cf. A005773, A047240, A047242, A057078, A136289, A204259.
Sequence in context: A336857 A049467 A131503 * A026309 A073936 A184811
Adjacent sequences: A047263 A047264 A047265 * A047267 A047268 A047269


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



