A259754 Numbers that are congruent to {3,9,15,18,21} mod 24.

3, 9, 15, 18, 21, 27, 33, 39, 42, 45, 51, 57, 63, 66, 69, 75, 81, 87, 90, 93, 99, 105, 111, 114, 117, 123, 129, 135, 138, 141, 147, 153, 159, 162, 165, 171, 177, 183, 186, 189, 195, 201, 207, 210, 213, 219, 225, 231, 234, 237, 243, 249, 255, 258, 261, 267

Offset

1,1

Comments

Original name: Numbers n such that n/A259748(n) = 3/2.

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

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

Formula

A259748(a(n))/a(n) = 2/3.

a(n) = 3*A047584(n). - Michel Marcus, Jul 18 2015

From Colin Barker, Aug 25 2016: (Start)

a(n) = a(n-1)+a(n-5)-a(n-6) for n>6.

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

(End)

Mathematica

A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}]; Select[Range[200], Mod[A[#], #]/# == 2/3 &]
Rest@ CoefficientList[Series[3 x (1 + x) (1 + x + x^2 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)), {x, 0, 56}], x] (* Michael De Vlieger, Aug 25 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {3, 9, 15, 18, 21, 27}, 60] (* Harvey P. Dale, Aug 30 2016 *)

Prog

(PARI) Vec(3*x*(1+x)*(1+x+x^2+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4)) + O(x^100)) \\ Colin Barker, Aug 25 2016

Crossrefs

Cf. A000914.

Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259749, A259750, A259751, A259752, A259755.

Sequence in context: A043381 A100331 A155764 * A277569 A310329 A310330

Adjacent sequences: A259751 A259752 A259753 * A259755 A259756 A259757

Keyword

nonn,easy

Author

José María Grau Ribas, Jul 12 2015

Extensions

Better name from Danny Rorabaugh, Oct 22 2015

Status

approved