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A027961
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a(n) = Lucas(n+2) - 3.
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13
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1, 4, 8, 15, 26, 44, 73, 120, 196, 319, 518, 840, 1361, 2204, 3568, 5775, 9346, 15124, 24473, 39600, 64076, 103679, 167758, 271440, 439201, 710644, 1149848, 1860495, 3010346, 4870844, 7881193, 12752040, 20633236, 33385279, 54018518
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(0) = 0, a(1) = 1, a(n) = a(n-1) + a(n-2) + 3.
a(n) = F(n) + F(n+2) - 3, n >= 2, where F(n) is the n-th Fibonacci number. - Zerinvary Lajos, Jan 31 2008
a(n) = Sum_{k=1..n} ((-1/phi)^k + (phi)^k) where phi = 1/2+1/2*sqrt(5). - Dimitri Papadopoulos, Jan 07 2016
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2]+3 od: seq(a[n], n=1..40); # Miklos Kristof, Mar 09 2005
with(combinat): seq(fibonacci(n)+fibonacci(n+2)-3, n=2..40); # Zerinvary Lajos, Jan 31 2008
g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-3, n=3..40); # Zerinvary Lajos, Jan 09 2009
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MATHEMATICA
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PROG
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(PARI) vector(40, n, fibonacci(n+3) +fibonacci(n+1) -3) \\ G. C. Greubel, Dec 18 2017
(PARI) first(n) = Vec(x*(1+2*x)/((1-x)*(1-x-x^2)) + O(x^(n+1))) \\ Iain Fox, Dec 19 2017
(Sage) [lucas_number2(n+2, 1, -1) -3 for n in (1..40)] # G. C. Greubel, Jun 01 2019
(GAP) List([1..40], n-> Lucas(1, -1, n+2)[2] -3 ) # G. C. Greubel, Jun 01 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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