A000970 Fermat coefficients.
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
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
- Vincenzo Librandi, Table of n, a(n) for n = 5..1000
- 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
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).
Crossrefs
Cf. A258708.
Programs
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Haskell
a000970 n = a258708 n (n - 5) -- Reinhard Zumkeller, Jun 23 2015
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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
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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 *) -
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
Formula
G.f.: x^5(3x^5 + 2x^4 + 4x^3 + 3x^2 + 3x + 1)/((1-x^5)(1-x)^4).
Extensions
More terms from Sean A. Irvine, Sep 25 2011