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A130236
Partial sums of the 'upper' Fibonacci Inverse A130234.
13
0, 1, 4, 8, 13, 18, 24, 30, 36, 43, 50, 57, 64, 71, 79, 87, 95, 103, 111, 119, 127, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 262, 272, 282, 292, 302, 312, 322, 332, 342, 352, 362, 372, 382, 392, 402, 412, 422, 432, 442, 452, 462, 473
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} A130234(k).
a(n) = n*A130234(n) - Fibonacci(A130234(n)+1) + 1.
G.f.: (x/(1-x)^2) * Sum_{k>=0} x^Fibonacci(k).
MATHEMATICA
b[n_]:= For[i=0, True, i++, If[Fibonacci[i] >= n, Return[i]]];
b/@ Range[0, 56]//Accumulate (* Jean-François Alcover, Apr 13 2020 *)
PROG
(Magma)
m:=120;
f:= func< x | x*(&+[x^Fibonacci(j): j in [0..Floor(3*Log(3*m+1))]])/(1-x)^2 >;
R<x>:=PowerSeriesRing(Rationals(), m+1);
[0] cat Coefficients(R!( f(x) )); // G. C. Greubel, Mar 18 2023
(SageMath)
m=120
def f(x): return x*sum( x^fibonacci(j) for j in range(1+int(3*log(3*m+1))))/(1-x)^2
def A130236_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(x) ).list()
A130236_list(m) # G. C. Greubel, Mar 18 2023
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, May 17 2007
STATUS
approved