A000971 Fermat coefficients.

1, 9, 42, 132, 334, 728, 1428, 2584, 4389, 7084, 10963, 16380, 23751, 33563, 46376, 62832, 83657, 109668, 141778, 181001, 228459, 285384, 353127, 433160, 527085, 636636, 763686, 910252, 1078500, 1270752, 1489488, 1737355, 2017169, 2331924

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• 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 = 6..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.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,19,-9,-9,18,-9,-9,19,-15,6,-1).

Crossrefs

Cf. A258708.

Programs

Haskell

a000971 n = a258708 n (n - 6)  -- Reinhard Zumkeller, Jun 23 2015

Maple

(1+3*z+3*z^7+z^8+3*z^2-4*z^3+10*z^4-4*z^5+3*z^6)/(z^6+z^3+1)/(-1+z)^6;

Mathematica

CoefficientList[Series[(1+3*x+3*x^7+x^8+3*x^2-4*x^3+10*x^4-4*x^5+3*x^6)/(x^6+x^3+1)/(-1+x)^6,{x,0,40}],x] (* Vincenzo Librandi, Mar 28 2012 *)

PARI

Vec((1+3*z+3*z^7+z^8+3*z^2-4*z^3+10*z^4-4*z^5+3*z^6)/(z^6+z^3+1)/(z-1)^6+O(x^99)) \\ Charles R Greathouse IV, Mar 28 2012

Formula

G.f.: (1 + 3x + 3x^7 + x^8 + 3x^2 - 4x^3 + 10x^4 - 4x^5 + 3x^6)/(x^6 + x^3 + 1)/(-1+x)^6 (see MAPLE line).

a(n) = A258708(n,n-6). - Reinhard Zumkeller, Jun 23 2015

Extensions

More terms from Sean A. Irvine, Sep 25 2011