The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A018910 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A018910

Pisot sequence L(4,5).
(history; published version)

#28 by Joerg Arndt at Sat Dec 30 23:42:53 EST 2023

STATUS

editing

approved

#27 by Paolo P. Lava at Sat Dec 30 12:06:16 EST 2023

FORMULA

a(n)=2+((5+2r5)/5)((1+r5)/2)^n+((5-2r5)/5)((1-r5)/2)^n, where r5 = sqrt(5).

- Paolo P. Lava, Jun 10 2008

STATUS

approved

editing

#26 by Bruno Berselli at Mon Dec 12 04:52:48 EST 2016

STATUS

proposed

approved

#25 by Jean-François Alcover at Mon Dec 12 04:39:49 EST 2016

STATUS

editing

proposed

#24 by Jean-François Alcover at Mon Dec 12 04:39:43 EST 2016

MATHEMATICA

LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* Jean-François Alcover, Dec 12 2016 *)

STATUS

approved

editing

#23 by N. J. A. Sloane at Sun Aug 07 11:25:25 EDT 2016

STATUS

proposed

approved

#22 by Colin Barker at Sun Aug 07 08:03:10 EDT 2016

STATUS

editing

proposed

#21 by Colin Barker at Sun Aug 07 08:02:45 EDT 2016

LINKS

Colin Barker, <a href="/A018910/b018910.txt">Table of n, a(n) for n = 0..1000</a>

PROG

(PARI) pisotL(nmax, a1, a2) = {

a=vector(nmax); a[1]=a1; a[2]=a2;

for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));

a

}

pisotL(50, 4, 5) \\ Colin Barker, Aug 07 2016

STATUS

approved

editing

#20 by R. J. Mathar at Tue Mar 22 12:05:31 EDT 2016

STATUS

editing

approved

#19 by R. J. Mathar at Tue Mar 22 12:05:25 EDT 2016

REFERENCES

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993;.

LINKS

D. W. Boyd, <a href="https://www.researchgate.net/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993

STATUS

approved

editing