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A002446 a(n) = 2^(2*n+1) - 2.
(Formerly M4193 N1748)
7
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
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
G.f.: 6*x/((1-x)*(1-4*x)). - 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, 30] (* 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..30]]; // Vincenzo Librandi, Jun 01 2011
(PARI) a(n) = 2*(4^n - 1); \\ G. C. Greubel, Jul 04 2019
(Sage) [2*(4^n -1) for n in (0..30)] # G. C. Greubel, Jul 04 2019
(GAP) List([0..30], n-> 2*(4^n - 1)) # G. C. Greubel, Jul 04 2019
CROSSREFS
Equals 6 * A002450(n).
A diagonal of the triangle in A241171.
Sequence in context: A366058 A356835 A344344 * A002934 A174319 A337456
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Jun 01 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)