A000971 Fermat coefficients. (Formerly M4623 N1975)

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

6,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A258708.

Sequence in context: A172464 A269053 A027441 * A061927 A292481 A051923

Adjacent sequences: A000968 A000969 A000970 * A000972 A000973 A000974

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Sep 25 2011

Status

approved