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A143212 a(n) = F(n) * (F(n+2)-1) = A000045(n) * A000071(n+2) = row sums of triangle A143211. 2
1, 2, 8, 21, 60, 160, 429, 1134, 2992, 7865, 20648, 54144, 141897, 371722, 973560, 2549421, 6675460, 17478176, 45761045, 119808150, 313668576, 821205937, 2149962768, 5628704256, 14736185425, 38579909330, 101003635304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to phi^2.

A143212(n) = Product of sum of first n Fibonacci numbers and Fibonacci number(n). - Vladimir Joseph Stephan Orlovsky, Oct 13 2009

LINKS

Table of n, a(n) for n=1..27.

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

FORMULA

a(n) = F(n) * (F(n+2)-1) = A000045(n) * A000071(n+2) = row sums of triangle A143211.

From R. J. Mathar, Sep 06 2008: (Start)

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

a(n) = -A000045(n+1) + 3*(-1)^n/5 + 7*A001906(n+1)/5 -3*A001906(n)/5. (End)

a(n) = F(n)*sum{k=0..n} F(k). - Paul Barry, Jan 05 2009

EXAMPLE

a(5) = 60 = F(5) * (F(7)-1) = 5*12.

a(5) = 60 = sum of row 5 terms of triangle A143211: (5 + 5 + 10 + 15 + 25).

MATHEMATICA

Clear[lst, n, a, f]; a=0; lst={}; Do[f=Fibonacci[n]; a+=f; AppendTo[lst, a*Fibonacci[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 13 2009 *)

Table[Fibonacci[n](Fibonacci[n+2]-1), {n, 30}] (* Harvey P. Dale, Dec 14 2012 *)

CROSSREFS

Cf. A000045, A000071, A143211.

Sequence in context: A123044 A143229 A123285 * A316270 A219970 A107361

Adjacent sequences:  A143209 A143210 A143211 * A143213 A143214 A143215

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 30 2008

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)