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A244309 a(n) = F(n)^3 - F(n)^2, where F(n) is the n-th Fibonacci number (A000045). 2
0, 0, 0, 4, 18, 100, 448, 2028, 8820, 38148, 163350, 697048, 2965248, 12595048, 53440504, 226608900, 960530634, 4070452764, 17246835648, 73069580980, 309555981900, 1311374255620, 5555264316910, 23532984885744, 99688652356608, 422291386890000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,2,-22,-4,14,-1,-1).

FORMULA

G.f.: 2*x^3*(x^2-x+2) / ((x+1)*(x^2-3*x+1)*(x^2-x-1)*(x^2+4*x-1)).

a(n) = A045991(A000045(n)). - Michel Marcus, Jun 25 2014

a(n) = (F(3*n) - 3*(-1)^n*F(n))/5 - (L(2*n) - 2*(-1)^n)/5, where F=A000045 and L=A000032. - Ehren Metcalfe, Mar 26 2016

EXAMPLE

a(4) is 18 because F(4)^3 - F(4)^2 = 3^3 - 3^2 = 18.

MATHEMATICA

CoefficientList[Series[2 x^3 (x^2 - x + 2)/((x + 1) (x^2 - 3 x + 1) (x^2 - x - 1) (x^2 + 4 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2014 *)

Table[#^3 - #^2 &@ Fibonacci@ n, {n, 0, 25}] (* Michael De Vlieger, Mar 27 2016 *)

LinearRecurrence[{5, 2, -22, -4, 14, -1, -1}, {0, 0, 0, 4, 18, 100, 448}, 30] (* Harvey P. Dale, Aug 22 2020 *)

PROG

(PARI) vector(50, n, fibonacci(n-1)^3-fibonacci(n-1)^2)

(Magma) [Fibonacci(n)^3 - Fibonacci(n)^2: n in [0..30]]; // Vincenzo Librandi, Jun 26 2014

CROSSREFS

Cf. A000045, A045991, A244310, A056570, A007598.

Sequence in context: A197593 A084832 A135177 * A137958 A215522 A201826

Adjacent sequences: A244306 A244307 A244308 * A244310 A244311 A244312

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jun 25 2014

STATUS

approved

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Last modified January 28 08:03 EST 2023. Contains 359850 sequences. (Running on oeis4.)