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A084508 Partial sums of A084509. Positions of ones in the first differences of A084506. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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).

FORMULA

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)

MATHEMATICA

LinearRecurrence[{5, -4}, {0, 1, 3, 9}, 30] (* Harvey P. Dale, May 21 2021 *)

CROSSREFS

Cf. A084506, A084509, A087289.

Sequence in context: A151041 A151042 A087289 * A151043 A151044 A247195

Adjacent sequences:  A084505 A084506 A084507 * A084509 A084510 A084511

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2003

STATUS

approved

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Last modified August 17 23:13 EDT 2022. Contains 356204 sequences. (Running on oeis4.)