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A047251 Numbers that are congruent to {1, 3, 4, 5} mod 6. 4
1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 67, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 87, 88, 89, 91, 93, 94, 95, 97, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

"Polyrhythmic Sequence" P(2,3): numbers congruent to 1 mod 2 and 1 mod 3. (See A267027 for definition and description). - Bob Selcoe, Jan 12 2016

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

FORMULA

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 3*n/2 - 1/2 - cos(Pi*n/2)/2.

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

a(n) = (-2-(-i)^n-i^n+6n)/4, with i=sqrt(-1). - Colin Barker, Oct 19 2015

From Wesley Ivan Hurt, May 31 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(2k) = A047270(k), a(2k-1) = A016777(k-1) for n>0. (End)

MAPLE

A047251:=n->(-2-(-I)^n-I^n+6*n)/4: seq(A047251(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

MATHEMATICA

Select[Range[0, 200], MemberQ[{1, 3, 4, 5}, Mod[#, 6]] &] (* Vincenzo Librandi, Jan 12 2016 *)

PROG

(PARI) a(n) = (-2-(-I)^n-I^n+6*n)/4 \\ Colin Barker, Oct 19 2015

(PARI) Vec(x*(x^3+x+1)/((x-1)^2*(x^2+1)) + O(x^100)) \\ Colin Barker, Oct 19 2015

(MAGMA) [n: n in [0..150]|n mod 6 in {1, 3, 4, 5}]; // Vincenzo Librandi, Jan 12 2016

CROSSREFS

Cf. A016777, A047270, A267027.

Sequence in context: A273670 A153329 A213637 * A258932 A183213 A183172

Adjacent sequences:  A047248 A047249 A047250 * A047252 A047253 A047254

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)