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A047250 Numbers that are congruent to {0, 3, 4, 5} mod 6. 1
0, 3, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 18, 21, 22, 23, 24, 27, 28, 29, 30, 33, 34, 35, 36, 39, 40, 41, 42, 45, 46, 47, 48, 51, 52, 53, 54, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 76, 77, 78, 81, 82, 83, 84, 87, 88, 89, 90, 93, 94, 95, 96, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is the interleaving of A047233 with A047270. - Guenther Schrack, Feb 15 2019

LINKS

Guenther Schrack, Table of n, a(n) for n = 1..10010

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

FORMULA

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

From Wesley Ivan Hurt, Jun 02 2016: (Start)

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

a(n) = (6*n - 3 + i^(2*n) - (1+i)*i^(-n) - (1-i)*i^n)/4 where i=sqrt(-1).

a(2*k) = A047270(k), a(2*k-1) = A047233(k). (End)

E.g.f.: (2 - sin(x) - cos(x) + (3*x - 2)*sinh(x) + (3*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, Jun 02 2016

From Guenther Schrack, Feb 15 2019: (Start)

a(n) = (6*n - 3 + (-1)^n - 2*(-1)^(n*(n-1)/2))/4.

a(n) = a(n-4) + 6, a(1)=0, a(2)=3, a(3)=4, a(4)=5, for n > 4.

a(-n) = -A047246(n+2). (End)

MAPLE

A047250:=n->(6*n-3+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/4: seq(A047250(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 3, 4, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 3, 4, 5, 6}, 60] (* Harvey P. Dale, Apr 01 2013 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 6 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 02 2016

(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(3+x+x^2+x^3)/((1+x)*(1+x^2)*(1-x)^2))) \\ G. C. Greubel, Feb 16 2019

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

CROSSREFS

Cf. A047233, A047246, A047270.

Complement: A047239.

Sequence in context: A333694 A338321 A220844 * A081944 A129948 A050414

Adjacent sequences:  A047247 A047248 A047249 * A047251 A047252 A047253

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)