A053438 Expansion of (1+x+2*x^3)/((1-x)*(1-x^2)).

1, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38, 39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99, 102, 103, 106, 107, 110, 111, 114, 115, 118, 119, 122

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = 2*n -(1+(-1)^n)/2 if n>=1. - Frank Ellermann, Feb 12 2002

a(n) = A042964(n), n>0. - R. J. Mathar, Oct 13 2008

a(n) = A014601(n) - 1 for n>0. - Hugo Pfoertner, Oct 26 2020

Maple

A053438 := proc(n)
    if n > 0 then
        2*n -(1+(-1)^n)/2 ;
    else
        1 ;
    end if
end proc:
seq(A053438(n), n=0..30) ; # R. J. Mathar, Oct 27 2020

Mathematica

CoefficientList[Series[(1+x+2*x^3)/((1-x)*(1-x^2)), {x, 0, 50}], x] (* or *) Join[{1}, LinearRecurrence[{1, 1, -1}, {2, 3, 6}, 50]] (* G. C. Greubel, May 26 2018 *)

Prog

(PARI) a(n)=abs(n\2*4+n%2*3-1) \\ Charles R Greathouse IV, Dec 08 2011
(Magma) I:=[2, 3, 6]; [1] cat [n le 3 select I[n] else Self(n-1) +Self(n-2) -Self(n-3): n in [1..30]]; // G. C. Greubel, May 26 2018

Crossrefs

Cf. A010684 (first differences), A263511 (partial sums).

Sequence in context: A335033 A107998 A276884 * A042964 A338064 A230375

Adjacent sequences: A053435 A053436 A053437 * A053439 A053440 A053441

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 12 2000

Status

approved