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

Author

Omar E. Pol, Sep 09 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A005843, A008585, A195014, A195019.

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

Programs

Haskell

import Data.List (transpose)
a195013 n = a195013_list !! (n-1)
a195013_list = concat $ transpose [[2, 4 ..], [3, 6 ..]]
-- Reinhard Zumkeller, Apr 06 2015

Magma

&cat[[2*n,3*n]: n in [1..34]]; // Bruno Berselli, Sep 25 2011

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 *)

PARI

a(n)=(5*n+(n-2)*(-1)^n+2)/4 \\ Charles R Greathouse IV, Sep 24 2015

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)