The On-Line Encyclopedia of Integer Sequences (OEIS)

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A116556

a(n) = 2*a(n-1) + 2*a(n-2), a(0)=0, a(1)=4.
(history; published version)

#32 by Joerg Arndt at Mon Jan 01 11:42:55 EST 2024

STATUS

editing

approved

#31 by Joerg Arndt at Mon Jan 01 11:42:43 EST 2024

MATHEMATICA

M = {{1, 1, 1, 1}, {1, 1, 0, 0}, {1, 0, 1, 0}, {1, 0, 0, 1}}; v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 25}]

#30 by Paolo P. Lava at Mon Jan 01 11:39:40 EST 2024

FORMULA

a(n) = (2/sqrt(3))*( [1+sqrt(3)]^n - [1-sqrt(3)]^n ), n>=0. - Paolo P. Lava, Jun 10 2008

STATUS

approved

editing

#29 by Bruno Berselli at Mon Oct 31 04:09:23 EDT 2016

STATUS

reviewed

approved

#28 by Joerg Arndt at Mon Oct 31 02:24:59 EDT 2016

STATUS

proposed

reviewed

#27 by Joerg Arndt at Mon Oct 31 02:24:56 EDT 2016

STATUS

editing

proposed

#26 by Joerg Arndt at Mon Oct 31 02:24:44 EDT 2016

KEYWORD

nonn,easy,less,changed

#25 by Joerg Arndt at Mon Oct 31 02:23:16 EDT 2016

FORMULA

Let M = {{1, 1, 1, 1}, {1, 1, 0, 0}, {1, 0, 1, 0}, {1, 0, 0, 1}}; v[1] = {0, 1, 1, 2}; v[n] = M.v[n - 1]; then a(n) =v[n][[1]]

STATUS

proposed

editing

#24 by Michel Marcus at Mon Oct 31 02:19:46 EDT 2016

STATUS

editing

proposed

#23 by Michel Marcus at Mon Oct 31 02:19:43 EDT 2016

LINKS

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.pdfhtml">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

STATUS

proposed

editing