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Revision History for A130244

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Partial sums of the 'upper' Lucas Inverse A130242.
(history; published version)

#8 by Charles R Greathouse IV at Thu Sep 08 08:45:30 EDT 2022

PROG

(MAGMAMagma) [0, 0] cat [(&+[Ceiling(Log(k + 1/2)/Log((1+Sqrt(5))/2)) : k in [0..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#7 by Bruno Berselli at Thu Sep 13 02:57:54 EDT 2018

STATUS

proposed

approved

#6 by Michel Marcus at Thu Sep 13 02:13:25 EDT 2018

STATUS

editing

proposed

#5 by Michel Marcus at Thu Sep 13 02:13:21 EDT 2018

FORMULA

G.f.: g(x) = x/(1-x)^2*(2*x^2 + Sum{k>=2, x^Lucas(k)}).

STATUS

proposed

editing

#4 by G. C. Greubel at Thu Sep 13 02:08:48 EDT 2018

STATUS

editing

proposed

#3 by G. C. Greubel at Thu Sep 13 02:08:20 EDT 2018

LINKS

G. C. Greubel, <a href="/A130244/b130244.txt">Table of n, a(n) for n = 0..2500</a>

FORMULA

a(n) = Sum_{k=0..n} A130242(k).

a(n) = n*A130242(n) - A000032(A130242(n) +1) for n>=3.

a(n)=sum{0<=k<=n, A130242(k)}=n*A130242(n)-A000032(A130242(n)+1) for n>=3. G.f.: g(x) = x/(1-x)^2*(2x2*x^2 +sum Sum{k>=2, x^Lucas(k)}).

MATHEMATICA

Join[{0, 0}, Table[Sum[Ceiling[Log[GoldenRatio, k + 1/2]], {k, 0, n}], {n, 1, 50}]] (* G. C. Greubel, Sep 12 2018 *)

PROG

(PARI) for(n=-1, 50, print1(if(n==-1, 0, if(n==0, 0, sum(k=0, n, ceil(log(k + 1/2)/log((1+sqrt(5))/2))))), ", ")) \\ G. C. Greubel, Sep 12 2018

(MAGMA) [0, 0] cat [(&+[Ceiling(Log(k + 1/2)/Log((1+Sqrt(5))/2)) : k in [0..n]]): n in [1..50]]; // G. C. Greubel, Sep 12 2018

STATUS

approved

editing

#2 by Russ Cox at Sat Mar 31 13:21:03 EDT 2012

AUTHOR

Hieronymus Fischer (_Hieronymus. Fischer(AT)gmx.de), _, May 19 2007

Discussion

Sat Mar 31

13:21

OEIS Server: https://oeis.org/edit/global/882

#1 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

NAME

Partial sums of the 'upper' Lucas Inverse A130242.

DATA

0, 0, 0, 2, 5, 9, 13, 17, 22, 27, 32, 37, 43, 49, 55, 61, 67, 73, 79, 86, 93, 100, 107, 114, 121, 128, 135, 142, 149, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390

OFFSET

0,4

FORMULA

a(n)=sum{0<=k<=n, A130242(k)}=n*A130242(n)-A000032(A130242(n)+1) for n>=3. G.f.: g(x)=x/(1-x)^2*(2x^2+sum{k>=2, x^Lucas(k)}).

CROSSREFS

Other related sequences: A000032, A130241, A130243, A130245, A130246, A130248, A130252, A130258, A130262. Fibonacci inverse see A130233 - A130240, A104162.

KEYWORD

nonn

AUTHOR

Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007

STATUS

approved