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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 09 2011
STATUS
approved