The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A138749 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A138749

a(n) = 2*a(n-1) - 5*a(n-2).
(history; published version)

#13 by N. J. A. Sloane at Sat Jul 11 02:32:50 EDT 2020

STATUS

proposed

approved

#12 by Michel Marcus at Sat Jul 11 00:14:07 EDT 2020

STATUS

editing

proposed

#11 by Michel Marcus at Sat Jul 11 00:14:03 EDT 2020

FORMULA

O.g.f.: -x*(1+5*x)/(1-2*x+5*x^2). a(n)=-A045873(n)-5*A045873(n-1). - _R. J. Mathar, _, Apr 03 2008

a(n) = (1/2)*(1+i)*((1+2*i)^n-i*(1-2*i)^n), where i=sqrt(-1) . - _Bruno Berselli, _, Jul 06 2011

PROG

(PARI) a(n)={local(v=Vec((1+2*I*x)^n)); sum(k=1, #v, real(v[k])-imag(v[k])); } /* cf. A116483 */ /* _Joerg Arndt_, Jul 06 2011 */

/* cf. A116483 */ /* Joerg Arndt, Jul 06 2011 */

STATUS

approved

editing

#10 by R. J. Mathar at Thu Jun 16 11:20:53 EDT 2016

STATUS

editing

approved

#9 by R. J. Mathar at Thu Jun 16 11:20:42 EDT 2016

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-5).

KEYWORD

sign,easy

EXTENSIONS

More terms from R. J. Mathar, Apr 03 2008

STATUS

approved

editing

#8 by Russ Cox at Fri Mar 30 17:39:33 EDT 2012

EXTENSIONS

More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Apr 03 2008

Discussion

Fri Mar 30

17:39

OEIS Server: https://oeis.org/edit/global/190

#7 by Russ Cox at Fri Mar 30 17:25:28 EDT 2012

AUTHOR

_Gary W. Adamson (qntmpkt(AT)yahoo.com), _, Mar 28 2008

Discussion

Fri Mar 30

17:25

OEIS Server: https://oeis.org/edit/global/135

#6 by Joerg Arndt at Wed Jul 06 05:26:32 EDT 2011

STATUS

proposed

approved

#5 by Joerg Arndt at Wed Jul 06 05:26:06 EDT 2011

FORMULA

a(n) = 2*a(n-1) - 5*a(n-2), n>3. a(n) = left term in [1,-2; 2,1]^n * [1,1].

a(n) = left term in [1,-2; 2,1]^n * [1,1].

O.g.f.: -x*(1+5*x)/(1-2*x+5*x^2). a(n)=-A045873(n)-5*A045873(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), , Apr 03 2008

#4 by Bruno Berselli at Wed Jul 06 05:23:49 EDT 2011

FORMULA

a(n) = (1/2)*(1+i)*((1+2*i)^n-i*(1-2*i)^n), where i=sqrt(-1) - Bruno Berselli, Jul 06 2011

STATUS

approved

proposed