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A047247 Numbers that are congruent to {2, 3, 4, 5} mod 6. 4
2, 3, 4, 5, 8, 9, 10, 11, 14, 15, 16, 17, 20, 21, 22, 23, 26, 27, 28, 29, 32, 33, 34, 35, 38, 39, 40, 41, 44, 45, 46, 47, 50, 51, 52, 53, 56, 57, 58, 59, 62, 63, 64, 65, 68, 69, 70, 71, 74, 75, 76, 77, 80, 81, 82, 83, 86, 87, 88, 89, 92, 93, 94, 95, 98, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence is the interleaving of A047235 with A047270. - Guenther Schrack, Feb 10 2019

LINKS

Guenther Schrack, Table of n, a(n) for n = 1..10015

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

Index entries for two-way infinite sequences

FORMULA

G.f.: x*(2+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(1-x)^2 ). - R. J. Mathar, Oct 08 2011

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

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

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

a(2*n) = A047270(n), a(2*n-1) = A047235(n).

a(n) = A047227(n) + 1, a(1-n) = - A047227(n). (End)

From Guenther Schrack, Feb 10 2019: (Start)

a(n) = (6*n - 1 - (-1)^n -2*(-1)^(n*(n+1)/2))/4.

a(n) = a(n-4) + 6, a(1)=2, a(2)=3, a(3)=4, a(4)=5, for n > 4.

a(n) = A047227(n) + 1. a(n) = A047246(n) + 2. (End)

MAPLE

A047247:=n->(6*n-1-I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/4: seq(A047247(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

MATHEMATICA

Table[(6n-1-I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)

PROG

(MAGMA) [n : n in [0..100] | n mod 6 in [2, 3, 4, 5]]; // Wesley Ivan Hurt, May 21 2016

(PARI) my(x='x+O('x^70)); Vec(x*(2+x+x^2+x^3+x^4)/((1-x)*(1-x^4))) \\ G. C. Greubel, Feb 16 2019

(Sage) a=(x*(2+x+x^2+x^3+x^4)/((1-x)*(1-x^4))).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019

CROSSREFS

Cf. A047227, A047235, A047246, A047270.

Complement: A047225.

Sequence in context: A046892 A068406 A276878 * A169606 A140769 A032877

Adjacent sequences:  A047244 A047245 A047246 * A047248 A047249 A047250

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 21 2016

STATUS

approved

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Last modified December 5 22:37 EST 2019. Contains 329782 sequences. (Running on oeis4.)