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A080143 a(n)=F(3)F(n)F(n+1)+F(4)F(n+1)^2-F(4) if n even, F(3)F(n)F(n+1)+F(4)F(n+1)^2 if n odd, where F(n) is the n-th Fibonacci number (A000045). 6
0, 5, 13, 39, 102, 272, 712, 1869, 4893, 12815, 33550, 87840, 229968, 602069, 1576237, 4126647, 10803702, 28284464, 74049688, 193864605, 507544125, 1328767775, 3478759198, 9107509824, 23843770272, 62423800997, 163427632717 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

S. Falcon, On the Sequences of Products of Two k-Fibonacci Numbers, American Review of Mathematics and Statistics, March 2014, Vol. 2, No. 1, pp. 111-120.

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f.: x*(5-2*x)/((1-x^2)*(1-3*x+x^2)), see a comment on A080144 for A(4,x). [Wolfdieter Lang, Jul 30 2012]

a(n)=sum(i=0, n, A000045(i+4)*A000045(i)) - Benoit Cloitre, Jun 14 2004

a(n) = (3*A027941(n) + 7*A001654(n))/2, n>=0. Proof: from the preceding sum given by B. Cloitre via recurrence on the first factor under the sum. See also A080097 and A059840(n+2). [From Wolfdieter Lang, Jul 27 21012]

MATHEMATICA

CoefficientList[Series[(5x+3x^2-2x^3)/((1-x^2)(1-2x-2x^2+x^3)), {x, 0, 30}], x]

CROSSREFS

Cf. A064831, A059840, A080097, A080144.

Sequence in context: A146062 A201612 A129924 * A077919 A272225 A272585

Adjacent sequences:  A080140 A080141 A080142 * A080144 A080145 A080146

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jan 30 2003

STATUS

approved

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Last modified December 4 23:10 EST 2016. Contains 278755 sequences.