A195013 Multiples of 2 and of 3 interleaved: a(2n-1) = 2n, a(2n) = 3n.

2, 3, 4, 6, 6, 9, 8, 12, 10, 15, 12, 18, 14, 21, 16, 24, 18, 27, 20, 30, 22, 33, 24, 36, 26, 39, 28, 42, 30, 45, 32, 48, 34, 51, 36, 54, 38, 57, 40, 60, 42, 63, 44, 66, 46, 69, 48, 72, 50, 75, 52, 78, 54, 81, 56, 84, 58, 87, 60, 90, 62, 93, 64, 96, 66, 99, 68, 102

Offset

1,1

Comments

First differences of A195014.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. H. Bailey, J. M. Borwein, and J. S. Kimberley, Discovery of large Poisson polynomials using a new arbitrary precision software package, Slides, 2015.

D. H. Bailey, J. M. Borwein, and J. S. Kimberley, Computer discovery and analysis of large Poisson polynomials, 2016.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

Pair(2*n, 3*n).

From Bruno Berselli, Sep 26 2011: (Start)

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

a(n) = (5*n+(n-2)*(-1)^n+2)/4.

a(n) = 2*a(n-2) - a(n-4) = a(n-2) + A010693(n-1).

a(n)+a(-n) = A010673(n).

a(n)-a(-n) = A106832(n). (End)

Mathematica

With[{r = Range[50]}, Riffle[2*r, 3*r]] (* or *)
LinearRecurrence[{0, 2, 0, -1}, {2, 3, 4, 6}, 100] (* Paolo Xausa, Feb 09 2024 *)

Prog

(Magma) &cat[[2*n, 3*n]: n in [1..34]]; // Bruno Berselli, Sep 25 2011
(Haskell)
import Data.List (transpose)
a195013 n = a195013_list !! (n-1)
a195013_list = concat $ transpose [[2, 4 ..], [3, 6 ..]]
-- Reinhard Zumkeller, Apr 06 2015
(PARI) a(n)=(5*n+(n-2)*(-1)^n+2)/4 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A005843, A008585, A195014, A195019.

Cf. A111712 (partial sums of this sequence prepended with 1).

Sequence in context: A092404 A094871 A157450 * A079667 A073061 A386846

Adjacent sequences: A195010 A195011 A195012 * A195014 A195015 A195016

Keyword

nonn,easy

Author

Omar E. Pol, Sep 09 2011

Status

approved