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A060925
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a(n) = 2a(n-1) + 3a(n-2), a(0) = 1, a(1) = 4.
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7
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1, 4, 11, 34, 101, 304, 911, 2734, 8201, 24604, 73811, 221434, 664301, 1992904, 5978711, 17936134, 53808401, 161425204, 484275611, 1452826834, 4358480501, 13075441504, 39226324511, 117678973534, 353036920601
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=charpoly(A,2). [From Milan R. Janjic (agnus(AT)blic.net), Jan 26 2010]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
| Row sums of Lucas convolution triangle A060922.
Inverse binomial transform of A003947. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
a(n)=sum(A060922(n, m), m=0..n) = sum(a(j-1)*A000204(n-j+1), j=1..n)+A000204(n+1).
a(n)=(5*3^n-(-1)^n)/4.
G.f.: (1+2*x)/(1-2*x-3*x^2).
a(2n) = 3a(2n-1) - 1; a(2n+1) = 3a(2n) + 1. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
Binomial transform is A003947. - Paul Barry (pbarry(AT)wit.ie), May 19 2003
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MATHEMATICA
| f[n_]:=3/(n+2); x=2; Table[x=f[x]; Denominator[x], {n, 0, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2010]
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PROG
| (PARI) { for (n=0, 200, write("b060925.txt", n, " ", (5*3^n - (-1)^n)/4); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 19 2009]
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CROSSREFS
| Sequence in context: A098324 A144791 A180305 * A027045 A006765 A151272
Adjacent sequences: A060922 A060923 A060924 * A060926 A060927 A060928
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
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EXTENSIONS
| Recurrence, now used as definition, from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 23 2005
Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Sep 10 2006
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