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A142964
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a(n) = 6*2^n - 2*n - 5.
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3
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1, 5, 15, 37, 83, 177, 367, 749, 1515, 3049, 6119, 12261, 24547, 49121, 98271, 196573, 393179, 786393, 1572823, 3145685, 6291411, 12582865, 25165775, 50331597, 100663243, 201326537, 402653127, 805306309, 1610612675, 3221225409, 6442450879, 12884901821
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OFFSET
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0,2
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COMMENTS
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Previous name was: One half of second column (m=1) of triangle A142963.
Essentially a duplicate of A050488. - Johannes W. Meijer, Feb 20 2009
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REFERENCES
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Eric Billault, Walter Damin, Robert Ferréol, Rodolphe Garin, MPSI Classes Prépas - Khôlles de Maths, Exercices corrigés, Ellipses, 2012, exercice 2.22 (1) pp 26, 43-44.
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LINKS
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Table of n, a(n) for n=0..31.
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
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FORMULA
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a(n) = A142693(n+2,1)/2.
From Johannes W. Meijer, Feb 20 2009: (Start)
a(n) = 4a(n-1) - 5a(n-2) + 2a(n-3) for n > 2 with a(0) = 1, a(1) = 5, a(2) = 15.
G.f.: (1+z)/((1-z)^2*(1-2*z)). (End)
a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^min(i,j) (Billault et al) (compare with A339771 that has max instead of min). - Bernard Schott, Dec 16 2020
a(n) = 2*A066524(n+1) - A339771(n). - Kevin Ryde, Dec 17 2020
E.g.f.: 6*exp(2*x) - exp(x)*(5 + 2*x). - Stefano Spezia, Dec 17 2020
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EXAMPLE
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a(3) = 6*2^3 - 2*3 - 5 = 37.
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MAPLE
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seq(6*2^n-2*n-5, n=0..40); # Bernard Schott, Dec 16 2020
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PROG
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(PARI) Vec((1+z)/((1-z)^2*(1-2*z)) + O(z^50)) \\ Michel Marcus, Jun 18 2017
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CROSSREFS
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Cf. A142965 (m=2 column/4).
Equals A050488(n+1).
Equals A156920(n+1,1).
Equals A156919(n+1,1)/2^n.
Cf. A156925, A339771.
Partial sums of A033484.
Sequence in context: A213487 A005491 A050488 * A188282 A014316 A075717
Adjacent sequences: A142961 A142962 A142963 * A142965 A142966 A142967
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Sep 15 2008
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EXTENSIONS
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New name using a formula of Bernard Schott by Peter Luschny, Dec 17 2020
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STATUS
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approved
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