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6, 13, 27, 55, 111, 223, 447, 895, 1791, 3583, 7167, 14335, 28671, 57343, 114687, 229375, 458751, 917503, 1835007, 3670015, 7340031, 14680063, 29360127, 58720255, 117440511, 234881023, 469762047, 939524095, 1879048191, 3758096383
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) = A164874(n+2,2); subsequence of A030130. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 29 2009]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-3, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^n*charpoly(A,-5). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
[a(n-1)]^2+a(n) = (7*2^(n-1))^2 are perfect squares. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
| a(n+1) = 2*a(n) + 1.
G.f.: (6-5*x)/((1-x)*(1-2*x)) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 14 2009]
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MATHEMATICA
| a=6; lst={a}; k=7; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 16 2008]
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CROSSREFS
| a(0) = 2 gives A153893, a(0)=3 essentially A126646.
a(0) = 4 gives A153894, a(0)=5 essentially A153893.
a(0) = 7 gives essentially A000225.
a(0) = 8 gives A052996 except initial terms, a(0) =9 essentially A153894.
a(0) = 10 gives A086225, a(0) = 11 essentially A153893.
a(0) = 13 essentially A086224.
Sequence in context: A192762 A183337 A173559 * A116913 A016071 A086652
Adjacent sequences: A086221 A086222 A086223 * A086225 A086226 A086227
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KEYWORD
| nonn,easy
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AUTHOR
| Marco Matosic (marcomatosic(AT)hotmail.com), Jul 27 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 22 2005
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