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A179006
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Partial sums of floor(Fibonacci(n)/4).
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1
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0, 0, 0, 0, 0, 1, 3, 6, 11, 19, 32, 54, 90, 148, 242, 394, 640, 1039, 1685, 2730, 4421, 7157, 11584, 18748, 30340, 49096, 79444, 128548, 208000, 336557, 544567, 881134, 1425711, 2306855, 3732576, 6039442, 9772030, 15811484
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OFFSET
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0,7
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COMMENTS
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) - a(n-7) + a(n-8).
a(n) = round(Fibonacci(n+2)/4 - n/3 - 3/8).
a(n) = round(Fibonacci(n+2)/4 - n/3 - 1/4).
a(n) = floor(Fibonacci(n+2)/4 - n/3 - 1/12).
a(n) = ceiling(Fibonacci(n+2)/4 - n/3 - 2/3).
a(n) = a(n-6) + Fibonacci(n-1) - 2, n > 6.
G.f.: -x^5/((x^2+x+1)*(x^2-x+1)*(x^2+x-1)*(x-1)^2).
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EXAMPLE
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a(7) = 0 + 0 + 0 + 0 + 0 + 1 + 2 + 3 = 6.
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MAPLE
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A179006 := proc(n) add( floor(combinat[fibonacci](i)/4), i=0..n) ; end proc:
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MATHEMATICA
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f[n_] := Floor[ Fibonacci@ n/4]; Accumulate@ Array[f, 38]
LinearRecurrence[{3, -3, 2, -2, 2, -1, -1, 1}, {0, 0, 0, 0, 0, 1, 3, 6}, 40] (* Harvey P. Dale, Jan 28 2020 *)
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PROG
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(PARI) a(n)={round(fibonacci(n+2)/4 - n/3 - 3/8)} \\ Andrew Howroyd, May 01 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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