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Search: id:A081057
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| A081057 |
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E.g.f.: sum(n>=0, a(n)*x^n/n!) = {sum(n>=0, F(n+1)*x^n/n!)}^2, where F(n) is the n-th Fibonacci number. |
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2
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| 1, 2, 6, 18, 58, 186, 602, 1946, 6298, 20378, 65946, 213402, 690586, 2234778, 7231898, 23402906, 75733402, 245078426, 793090458, 2566494618, 8305351066, 26876680602, 86974765466, 281456253338, 910811568538, 2947448150426
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OFFSET
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0,2
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COMMENT
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a(n) ~ c*(sqrt(5)+1)^n, where c=(sqrt(5)+3)/10.
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FORMULA
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G.f.: (1-x-2x^2)/(1-3x-2x^2+4x^3). - Michael Somos, Mar 04 2003
a(n) - 2*a(n-1) = A014334(n), n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 05 2003
a(n) = 2/5+(3/10-1/10*5^(1/2))*(1-5^(1/2))^n+(3/10+1/10*5^(1/2))*(1+5^(1/2))^n. Recurrence: a(n) = 3*a(n-1)+2*a(n-2)-4*a(n-3). G.f.: (1+x)*(1-2*x)/(1-2*x-4*x^2)/(1-x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 05 2003
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CROSSREFS
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a(n) = A052899(n-1) + A052899(n). a(n) - 2*a(n-1) = A014334(n).
Sequence in context: A125305 A148458 A148459 this_sequence A000137 A151282 A157004
Adjacent sequences: A081054 A081055 A081056 this_sequence A081058 A081059 A081060
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Mar 03 2003
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs) and Michael Somos, Mar 05 2003
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