A106469 Expansion of (1 + x^2)*(1 + 2*x)/(1 - x^2).

1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4

Offset

0,2

Comments

From Elmo R. Oliveira, Oct 07 2025: (Start)

A040003 preceded by 1.

Decimal expansion of 101/825.

Continued fraction expansion of 1 + sqrt(1/6). (End)

Links

Table of n, a(n) for n=0..95.

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

Formula

a(0)=1, a(n) = (2 - 0^((n-1)/2))*(1 - (-1)^n) + (2 - 0^(n/2))*(1 + (-1)^n)/2, n>0.

From Elmo R. Oliveira, Oct 07 2025: (Start)

E.g.f.: 2*cosh(x) + 4*sinh(x) - 2*x - 1.

a(n) = a(n-2) for n > 3. (End)

Mathematica

CoefficientList[Series[(1+x^2)(1+2x)/(1-x^2), {x, 0, 95}], x] (* James C. McMahon, Feb 02 2024 *)

Crossrefs

Row sums of A106468.

Cf. A040003.

Essentially the same as A105397 and A010694.

Sequence in context: A100374 A045841 A040003 * A082508 A327730 A365348

Adjacent sequences: A106466 A106467 A106468 * A106470 A106471 A106472

Keyword

easy,nonn

Author

Paul Barry, May 03 2005

Status

approved