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A047227 Numbers that are congruent to {1, 2, 3, 4} mod 6. 4
1, 2, 3, 4, 7, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 22, 25, 26, 27, 28, 31, 32, 33, 34, 37, 38, 39, 40, 43, 44, 45, 46, 49, 50, 51, 52, 55, 56, 57, 58, 61, 62, 63, 64, 67, 68, 69, 70, 73, 74, 75, 76, 79, 80, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 97, 98 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

From Johannes W. Meijer, Jul 07 2011: (Start)

a(n) = floor((n+2)/4) + floor((n+1)/4) + floor(n/4) + 2*floor((n-1)/4) + floor((n+3)/4).

G.f.: x*(1+x+x^2+x^3+2*x^4)/(x^5-x^4-x+1). (End)

From Wesley Ivan Hurt, May 20 2016: (Start)

a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.

a(n) = (6n-5-i^(2n)+(1+i)*i^(1-n)+(1-i)*i^(n-1))/4 where i=sqrt(-1).

a(2n) = A047235(n), a(2n-1) = A047241(n). (End)

E.g.f.: (4 + sin(x) - cos(x) + (3*x - 2)*sinh(x) + 3*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 21 2016

From Wesley Ivan Hurt, May 21 2016: (Start)

a(n) = A047246(n) + 1.

a(n+2)-a(n+1) = A093148(n) for n>0.

a(1-n) = - A047247(n). (End)

MAPLE

A047227:=n->(6*n-5-I^(2*n)+(1+I)*I^(1-n)+(1-I)*I^(n-1))/4: seq(A047227(n), n=1..100); # Wesley Ivan Hurt, May 20 2016

MATHEMATICA

Complement[Range[100], Flatten[Table[{6n - 1, 6n}, {n, 0, 15}]]] (* Alonso del Arte, Jul 07 2011 *)

Select[Range[100], MemberQ[{1, 2, 3, 4}, Mod[#, 6]]&] (* Vincenzo Librandi, Jan 06 2013 *)

PROG

(MAGMA) [n: n in [0..100] | n mod 6 in [1..4]]; // Vincenzo Librandi, Jan 06 2013

CROSSREFS

Cf. A008621, A047235, A047241, A047245, A047246, A047247, A093148.

Complement of A047264. Equals A203016 divided by 3.

Sequence in context: A096199 A104576 A031477 * A317047 A228102 A261412

Adjacent sequences:  A047224 A047225 A047226 * A047228 A047229 A047230

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)