A256233 a(n) = L(2*n+1) - 2, where L is A000032.

-1, 2, 9, 27, 74, 197, 519, 1362, 3569, 9347, 24474, 64077, 167759, 439202, 1149849, 3010347, 7881194, 20633237, 54018519, 141422322, 370248449, 969323027, 2537720634, 6643838877, 17393795999, 45537549122, 119218851369, 312119004987, 817138163594

Offset: 0

Author

Vincenzo Librandi, Mar 20 2015

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Crossrefs

Cf. A000032, A004146.

Programs

Magma

[Lucas(n)-2: n in [1..70 by 2]];

Mathematica

Table[LucasL[n] - 2, {n, 1, 70, 2}] (* or *) LinearRecurrence[{4, -4, 1}, {-1, 2, 9}, 40]

PARI

Vec((-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Nov 03 2016

PARI

L(n) = round(((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n)
vector(30, n, n--; L(2*n+1)-2) \\ Colin Barker, Nov 03 2016

Formula

G.f.: (-1+6*x-3*x^2)/((1-x)*(1-3*x+x^2)).

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).

a(n) = (-2+(2^(-1-n)*((3-sqrt(5))^n*(-5+sqrt(5))+(3+sqrt(5))^n*(5+sqrt(5))))/sqrt(5)). - Colin Barker, Nov 03 2016

Extensions

Incorrect comment about A004146 removed by Georg Fischer, Sep 04 2020