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Search: id:A007689
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| A007689 |
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2^n + 3^n.
(Formerly M1444)
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+0
63
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| 2, 5, 13, 35, 97, 275, 793, 2315, 6817, 20195, 60073, 179195, 535537, 1602515, 4799353, 14381675, 43112257, 129271235, 387682633, 1162785755, 3487832977, 10462450355, 31385253913, 94151567435, 282446313697, 847322163875
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 92.
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 14.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 169
Zerinvary Lajos, Sage Notebooks
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FORMULA
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E.g.f.: exp(2*x)*(1+exp(x)). G.f.: (2-5*x)/((1-2*x)*(1-3*x)). a(n) = 5*a(n-1)-6*a(n-2).
2 + 5 + 13 + 35 +...n terms = (1/2)*(3^n - 1)+(2^n - 1). [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 20 2006
Equals double binomial transform of [2, 1, 1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
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MATHEMATICA
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Table[2^n + 3^n, {n, 0, 25}]
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PROGRAM
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sage: [lucas_number2(n, 5, 6)for n in xrange(0, 27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Binomial transform of A000051. Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.
Sequence in context: A005773 A022855 A091190 this_sequence A085281 A082582 A086581
Adjacent sequences: A007686 A007687 A007688 this_sequence A007690 A007691 A007692
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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Additional comments from Michael Somos, Jun 10, 2000.
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