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#26 by Michael De Vlieger at Sun May 26 08:25:04 EDT 2024
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#25 by Michel Marcus at Sun May 26 06:02:15 EDT 2024
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#24 by Stefano Spezia at Sun May 26 05:49:27 EDT 2024
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#23 by Stefano Spezia at Sun May 26 05:02:27 EDT 2024
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E.g.f.: cosh(x) - sinh(x) + exp(x)*sinh(sqrt(2)*x)/sqrt(2). - Stefano Spezia, May 26 2024
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approved
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#22 by Michel Marcus at Mon Mar 11 04:38:34 EDT 2024
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#21 by Joerg Arndt at Mon Mar 11 04:35:59 EDT 2024
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#20 by Michel Marcus at Mon Mar 11 03:49:39 EDT 2024
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#19 by Michel Marcus at Mon Mar 11 03:49:37 EDT 2024
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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, ,3, ,1).
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G.f. (.: (x-1)/((x+1)*(x^2+2*x-1)).
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proposed
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#18 by Joerg Arndt at Mon Mar 11 02:00:50 EDT 2024
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#17 by Joerg Arndt at Mon Mar 11 02:00:45 EDT 2024
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a(n) = a(n-1) + 3*a(n-2) + a(n-3), n >= 3; G.f. (x-1)/((x+1)*(x^2+2*x-1)); a(n) = (sqrt(2)/4)*((1 + sqrt(2))^n - (1 - sqrt(2))^n)) + (-1)^n;
G.f.: G(0)/(2+2*x), where G(k)= 1 + 1/(1 - (x)*(2*k-1)/((x)*(2*k+1) - 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 10 2013
G.f. (x-1)/((x+1)*(x^2+2*x-1)).
a(n) = (sqrt(2)/4)*((1 + sqrt(2))^n - (1 - sqrt(2))^n)) + (-1)^n.
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reviewed
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