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Search: id:A126566
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| A126566 |
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a(0)=1; a(1)=2; a(2)=5; a(3)=14; for n>3: a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-a(n-4). |
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+0
4
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| 1, 2, 5, 14, 43, 142, 495, 1794, 6681, 25346, 97357, 377038, 1468019, 5735758, 22460935, 88083586, 345754097, 1358000258, 5335796565, 20970349326, 82429113339, 324040664974, 1273932845663, 5008544929922, 19691924052361
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OFFSET
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0,2
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COMMENT
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a(n) is also the first entry of the vector M^n*[1,0,0,0], where M is the type F_4 Cartan matrix [[2,-1,0,0]; [ -1,2,-2,0]; [0,-1,2,-1]; [0,0,-1,2]].
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FORMULA
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G.f.: -(2*x-1)*(x^2-4*x+1)/(1-8*x+20*x^2-16*x^3+x^4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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MATHEMATICA
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a = {1, 2, 5, 14}; Do[AppendTo[a, 8*a[[ -1]]-20*a[[ -2]]+16*a[[ -3]]-a[[ -4]]], {24}]; a
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CROSSREFS
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Cf. A126569.
Sequence in context: A029889 A123020 A005317 this_sequence A112808 A088927 A110489
Adjacent sequences: A126563 A126564 A126565 this_sequence A126567 A126568 A126569
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2006
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EXTENSIONS
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Edited and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Aug 12 2007
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