The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A153593 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A153593

a(n) = ((9 + sqrt(2))^n - (9 - sqrt(2))^n)/(2*sqrt(2)).
(history; published version)

#31 by Charles R Greathouse IV at Thu Sep 08 08:45:40 EDT 2022

PROG

(MAGMAMagma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008

Discussion

Thu Sep 08

08:45

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

#30 by Alois P. Heinz at Sat Aug 12 06:46:55 EDT 2017

STATUS

reviewed

approved

#29 by Michel Marcus at Sat Aug 12 06:21:32 EDT 2017

STATUS

proposed

reviewed

#28 by Ilya Gutkovskiy at Sat Aug 12 06:05:56 EDT 2017

STATUS

editing

proposed

#27 by Ilya Gutkovskiy at Sat Aug 12 05:59:49 EDT 2017

FORMULA

E.g.f.: exp(9*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

STATUS

approved

editing

#26 by Michel Marcus at Tue Aug 23 03:53:57 EDT 2016

STATUS

reviewed

approved

#25 by Joerg Arndt at Tue Aug 23 02:25:11 EDT 2016

STATUS

proposed

reviewed

#24 by Michel Marcus at Mon Aug 22 23:24:13 EDT 2016

STATUS

editing

proposed

#23 by Michel Marcus at Mon Aug 22 23:24:08 EDT 2016

REFERENCES

S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.

LINKS

S. Falcon, <a href="http://dx.doi.org/10.9734/BJMCS/2014/11783">Iterated Binomial Transforms of the k-Fibonacci Sequence</a>, British Journal of Mathematics & Computer Science, 4 (22): 2014.

#22 by Michel Marcus at Mon Aug 22 23:21:43 EDT 2016

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [_// _Klaus Brockhaus_, Dec 31 2008]

STATUS

proposed

editing