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A094586 Central numbers of the triangle T of all positive differences of distinct Fibonacci numbers. 2
1, 5, 16, 47, 131, 356, 953, 2529, 6676, 17567, 46135, 121016, 317201, 831053, 2176712, 5700303, 14926171, 39081404, 102323209, 267896585, 701380076, 1836265535, 4807451951, 12586147632, 32951083681, 86267253461, 225850919488 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As T is also the triangle of sums of consecutive distinct Fibonacci numbers, a(n) is such a sum, namely Sum_{j=n+1..2n} Fibonacci(j).

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..2000

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

FORMULA

a(n) = Fibonacci(2n+2) - Fibonacci(n+2) = A094585(2n-1, n).

G.f.: x*(1+x-x^2)/((1-x-x^2)*(1-3*x+x^2)). - Colin Barker, Sep 16 2012

EXAMPLE

a(4) = F(10)-F(6) = 55-8 = 47.

MATHEMATICA

Table[Sum[Fibonacci[n+i], {i, n}], {n, 30}] (* Zerinvary Lajos, Jul 12 2009 *)

With[{F=Fibonacci}, Table[F[2n+2]-F[n+2], {n, 30}]] (* G. C. Greubel, Jul 14 2019 *)

PROG

(GAP) List([1..30], n->Fibonacci(2*n+2)-Fibonacci(n+2)); # Muniru A Asiru, Apr 28 2019

(PARI) vector(30, n, f=fibonacci; f(2*n+2)-f(n+2)) \\ G. C. Greubel, Jul 14 2019

(MAGMA) F:=Fibonacci; [F(2*n+2)-F(n+2): n in [1..30]]; // G. C. Greubel, Jul 14 2019

(Sage) f=fibonacci; [f(2*n+2)-f(n+2) for n in (1..30)] # G. C. Greubel, Jul 14 2019

CROSSREFS

Cf. A000045, A094585.

Sequence in context: A086750 A086749 A194541 * A140336 A197201 A166868

Adjacent sequences:  A094583 A094584 A094585 * A094587 A094588 A094589

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 13 2004

STATUS

approved

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Last modified May 31 10:52 EDT 2020. Contains 334748 sequences. (Running on oeis4.)