A084508 - OEIS

A084508

Partial sums of A084509. Positions of ones in the first differences of A084506.

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