login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002446 2^(2n+1) - 2.
(Formerly M4193 N1748)
6
0, 6, 30, 126, 510, 2046, 8190, 32766, 131070, 524286, 2097150, 8388606, 33554430, 134217726, 536870910, 2147483646, 8589934590, 34359738366, 137438953470, 549755813886, 2199023255550, 8796093022206, 35184372088830 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 283.

A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.

S. A. Joffe, Calculation of the first thirty-two Eulerian numbers from central differences of zero, Quart. J. Pure Appl. Math. 47 (1914), 103-126.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (5,-4).

FORMULA

G.f.: 6*x/(4*x-1)/(x-1). - Simon Plouffe, see MAPLE line

E.g.f.: (cos(i*x)-1)^2. - Vladimir Kruchinin, Oct 28 2012

MAPLE

A002446:=6*z/((4*z-1)*(z-1)); [Generating function. Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

f[n_] := Det[{{1, 1}, {1, 4}}^(n - 1) {{1, 2}, {1, 2}}]; Array[f, 23] (* Robert G. Wilson v, Jul 13 2011 *)

2^(2*Range[0, 30]+1)-2 (* or *) LinearRecurrence[{5, -4}, {0, 6}, 30] (* Harvey P. Dale, Sep 01 2016 *)

PROG

(MAGMA) [2^(2*n+1) - 2: n in [0..25]]; // Vincenzo Librandi, Jun 01 2011

CROSSREFS

Equals 6 * A002450(n). A diagonal of the triangle in A241171.

Sequence in context: A073970 A074009 A248328 * A002934 A174319 A131458

Adjacent sequences:  A002443 A002444 A002445 * A002447 A002448 A002449

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Jun 01 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 12:46 EST 2018. Contains 299623 sequences. (Running on oeis4.)