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A000970
Fermat coefficients.
(Formerly M4386 N1846)
2
1, 7, 25, 66, 143, 273, 476, 775, 1197, 1771, 2530, 3510, 4750, 6293, 8184, 10472, 13209, 16450, 20254, 24682, 29799, 35673, 42375, 49980, 58565, 68211, 79002, 91025, 104371, 119133, 135408, 153296, 172900, 194327, 217686, 243090, 270655
OFFSET
5,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
LINKS
R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.
P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.
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.: x^5(3x^5 + 2x^4 + 4x^3 + 3x^2 + 3x + 1)/((1-x^5)(1-x)^4).
a(n) = A258708(n,n-5) = A258708(2*n-7,2). - Reinhard Zumkeller, Jun 23 2015
MAPLE
A000970:=-(2*z**4+3*z**5+3*z**2+4*z**3+3*z+1)/(z**4+z**3+z**2+z+1)/(z-1)**5; # Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[(3x^5+2x^4+4x^3+3x^2+3x+1)/((1-x^5)(1-x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 28 2012 *)
LinearRecurrence[{4, -6, 4, -1, 1, -4, 6, -4, 1}, {1, 7, 25, 66, 143, 273, 476, 775, 1197}, 40] (* Harvey P. Dale, Sep 06 2017 *)
PROG
(PARI) Vec((3*x^5+2*x^4+4*x^3+3*x^2+3*x+1)/(1-x^5)/(1-x)^4+O(x^99)) \\ Charles R Greathouse IV, Mar 28 2012
(Haskell)
a000970 n = a258708 n (n - 5) -- Reinhard Zumkeller, Jun 23 2015
CROSSREFS
Cf. A258708.
Sequence in context: A056685 A299262 A001296 * A247620 A240156 A155245
KEYWORD
nonn,easy
EXTENSIONS
More terms from Sean A. Irvine, Sep 25 2011
STATUS
approved