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Search: id:A018215
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| 0, 4, 32, 192, 1024, 5120, 24576, 114688, 524288, 2359296, 10485760, 46137344, 201326592, 872415232, 3758096384, 16106127360, 68719476736, 292057776128, 1236950581248, 5222680231936, 21990232555520
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Bisection of A001787. That is, a(n)=A001787(2n) - Graeme McRae (g_m(AT)mcraefamily.com), Jul 12 2006
All numbers of the form n*4^n+(4^n-1)/3 have the property that they are sums of two squares and also their indices are the sum of two squares. This follows from the identity n*4^n+(4^n-1)/3=4(4(..4(4n+1)+1)+1)+1..)+1. - Artur Jasinski (grafix(AT)csl.pl), Nov 12 2007
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FORMULA
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G.f.: 4*x/(1-4*x)^2. E.g.f.: 4*x*exp(4*x).
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MAPLE
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seq(add((count(Composition(n)))^2, k=2..n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 17 2006
with(finance):seq(futurevalue(n, 3, n), n=0..20); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 4, 0)*binomial(n, 1) for n in xrange(0, 26)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
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CROSSREFS
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Cf. A002450.
Sequence in context: A112850 A113154 A083299 this_sequence A099133 A043018 A002012
Adjacent sequences: A018212 A018213 A018214 this_sequence A018216 A018217 A018218
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Peter Winkler (pw(AT)bell-labs.com)
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