Revision History for A117110
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#14 by Joerg Arndt at Mon Jan 01 11:42:14 EST 2024
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#13 by Joerg Arndt at Mon Jan 01 11:42:09 EST 2024
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| NAME
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The (1,1)-entry of the vector v[n]=Mv[n-1], where M is the 3 x 3 matrix [[0,-1/r,r],[ -1/r,-2/r,1],[r,1,2+2/r]], r being the golden ratio and v[0] is the column matrix [0,1,1].
Expansion of x*(1+5*x)/((1+2*x+1)*(1-4*x)).
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| COMMENTS
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Characteristic polynomial of the matrix M is x(x^2-2x-8).
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| FORMULA
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Recurrence relation: a(n)=2a) = 2*a(n-1)+8a) + 8*a(n-2) for n>=3; a(0)=0,, a(1)=1,, a(2)=7.
O.g.f.: -.: x*(1+5*x)/((1+2*x+1)*(1-4*x-1)). - R. J. Mathar, Dec 05 2007
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| MAPLE
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with(linalg): r:=(1+sqrt(5))/2: M:=matrix(3, 3, [0, -1/r, r, -1/r, -2/r, 1, r, 1, 2+2/r]): v[0]:=matrix(3, 1, [0, 1, 1]): for n from 1 to 26 do v[n]:=simplify(multiply(M, v[n-1])) od: seq(simplify(rationalize(v[n][1, 1])), n=0..26);
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nonn,easy,changed
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| EXTENSIONS
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New name using g.f. from Joerg Arndt, Jan 01 2024
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| STATUS
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approved
editing
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#12 by Joerg Arndt at Mon Jan 01 11:40:34 EST 2024
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#11 by Paolo P. Lava at Mon Jan 01 11:39:57 EST 2024
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a(n)=-(1/2)*(-2)^(n-1)+(3/2)*4^(n-1)-5/8*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Oct 07 2008]
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approved
editing
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#10 by Russ Cox at Fri Mar 30 18:53:35 EDT 2012
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a(n)=-(1/2)*(-2)^(n-1)+(3/2)*4^(n-1)-5/8*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava (paoloplava(AT)gmail.com), _, Oct 07 2008]
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Discussion
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| Fri Mar 30
| 18:53
| OEIS Server: https://oeis.org/edit/global/262
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#9 by Russ Cox at Fri Mar 30 17:39:11 EDT 2012
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| FORMULA
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O.g.f.: -x*(1+5*x)/((2*x+1)*(4*x-1)). - )). - _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Dec 05 2007
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Discussion
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| Fri Mar 30
| 17:39
| OEIS Server: https://oeis.org/edit/global/190
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#8 by Russ Cox at Fri Mar 30 17:34:20 EDT 2012
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| AUTHOR
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_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Apr 18 2006
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Discussion
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| Fri Mar 30
| 17:34
| OEIS Server: https://oeis.org/edit/global/158
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#7 by Russ Cox at Fri Mar 30 16:50:24 EDT 2012
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Edited by _N. J. A. Sloane (njas(AT)research.att.com), _, May 13 2006
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Discussion
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| Fri Mar 30
| 16:50
| OEIS Server: https://oeis.org/edit/global/110
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#6 by T. D. Noe at Wed Sep 28 20:48:35 EDT 2011
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a(n)=-(1/2)*(-2)^(n-1)+(3/2)*4^(n-1)-5/8*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (pplpaoloplava(AT)splgmail.atcom), Oct 07 2008]
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Discussion
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| Wed Sep 28
| 20:48
| OEIS Server: https://oeis.org/edit/global/96
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#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009
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| NAME
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The (1,1)-entry of the vector v[n]=Mv[n-1], where M is the 3 x 3 matrix [[0,-1/r,r],[ -1/r,-2/r,1],[r,1,2+2/r]], r being the golden ratio, and v[0] is the column matrix [0,1,1].
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nonn,new
nonn
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| EXTENSIONS
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Edited by N. J. A. Sloane (njas, (AT)research.att.com), May 13 2006
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