A136488 a(n) = 2^n - A005418(n).

1, 2, 5, 10, 22, 44, 92, 184, 376, 752, 1520, 3040, 6112, 12224, 24512, 49024, 98176, 196352, 392960, 785920, 1572352, 3144704, 6290432, 12580864, 25163776, 50327552, 100659200, 201318400, 402644992, 805289984, 1610596352, 3221192704, 6442418176, 12884836352

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-4).

Formula

a(n) = 2^n - A005418(n). Sum of (n-1)-th row terms of triangle A136482.

G.f.: x*(1 - x^2)/(1 - 2*x - 2*x^2 + 4*x^3). - Michael De Vlieger, Sep 23 2016

From Colin Barker, Sep 23 2016: (Start)

a(n) = 3*2^(n-2)-2^(n/2-1) for n even.

a(n) = 3*2^(n-2)-2^((n-3)/2) for n odd.

(End)

a(n) = A135098(n-1) for n >= 1. - Georg Fischer, Nov 02 2018

Example

a(5) = 22 = 2^5 - A005418(5) = 32 - 10.
a(5) = 22 = sum of row 5 terms of triangle A136482 = (1 + 6 + 8 + 6 + 1).

Mathematica

Table[2^n - (2^(n - 2) + 2^(Floor[n/2] - 1)), {n, 40}] (* after Harvey P. Dale at A005418, or *)
CoefficientList[Series[(1 - x^2)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 40}], x] (* Michael De Vlieger, Sep 23 2016 *)

Prog

(PARI) Vec(x*(1-x)*(1+x)/((1-2*x)*(1-2*x^2)) + O(x^40)) \\ Colin Barker, Sep 23 2016
(Magma) [2^n - (2^(n - 2) + 2^(Floor(n/2) - 1)): n in [1..40]]; // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A005418, A135098, A136482.

Sequence in context: A093370 A094537 A135098 * A045621 A026655 A336484

Adjacent sequences: A136485 A136486 A136487 * A136489 A136490 A136491

Keyword

nonn,easy

Author

Gary W. Adamson, Jan 01 2008

Extensions

More terms from Colin Barker, Mar 19 2013

Missing a(4) added by Michael De Vlieger, Sep 23 2016

Status

approved