login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182780 Twice A024537. 4
2, 4, 8, 18, 42, 100, 240, 578, 1394, 3364, 8120, 19602, 47322, 114244, 275808, 665858, 1607522, 3880900, 9369320, 22619538, 54608394, 131836324, 318281040, 768398402, 1855077842, 4478554084, 10812186008, 26102926098, 63018038202, 152139002500, 367296043200, 886731088898, 2140758220994, 5168247530884 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n) = A078057(n) + 1 (see A288213). - Michel Dekking, Sep 29 2019
LINKS
J. V. Leyendekkers and A. G. Shannon, Pellian sequence relationships among pi, e, sqrt(2), Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 58-62. See Table 2.
FORMULA
From Colin Barker, May 26 2018: (Start)
G.f.: 2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)).
a(n) = (2 + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.
a(n) = 3*a(n-1) - a(n-2) - a(n-3) for n>2.
(End)
PROG
(PARI) Vec(2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)) + O(x^40)) \\ Colin Barker, May 26 2018
(Magma) a:=[2, 4, 8]; [n le 3 select a[n] else 3*Self(n-1) - Self(n-2) - Self(n-3):n in [1..35]]; // Marius A. Burtea, Sep 29 2019
CROSSREFS
Cf. A024537.
Sequence in context: A306200 A057151 A026699 * A078678 A261492 A027056
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 23 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)