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A084508
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Partial sums of A084509. Positions of ones in the first differences of A084506.
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5
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0, 1, 3, 9, 33, 129, 513, 2049, 8193, 32769, 131073, 524289, 2097153, 8388609, 33554433, 134217729, 536870913, 2147483649, 8589934593, 34359738369, 137438953473, 549755813889, 2199023255553, 8796093022209, 35184372088833
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..24.
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (5,-4).
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FORMULA
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a(n) = n for n < 2, a(n) = 2^(2*n - 3) + 1 = A087289(n-2) for n >= 2. - Antti Karttunen, Oct 24 2012 [Corrected by Petros Hadjicostas, Aug 02 2020]
From Chai Wah Wu, Jan 28 2021: (Start)
a(n) = 5*a(n-1) - 4*a(n-2) for n > 3.
G.f.: x*(-2*x^2 - 2*x + 1)/((x - 1)*(4*x - 1)). (End)
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MATHEMATICA
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LinearRecurrence[{5, -4}, {0, 1, 3, 9}, 30] (* Harvey P. Dale, May 21 2021 *)
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CROSSREFS
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Cf. A084506, A084509, A087289.
Sequence in context: A151041 A151042 A087289 * A151043 A151044 A247195
Adjacent sequences: A084505 A084506 A084507 * A084509 A084510 A084511
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jun 02 2003
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STATUS
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approved
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