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A000970

Fermat coefficients.
(Formerly M4386 N1846)

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 (list; graph; refs; listen; history; text; internal format)

	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	`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).`
	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:=-(2z4+3z*5+3z*2+4z*3+3z+1)/(z4+z3+z2+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((3x^5+2x^4+4x^3+3x^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` `Adjacent sequences: A000967 A000968 A000969 * A000971 A000972 A000973`
	KEYWORD	`nonn,easy`
	AUTHOR	`N. J. A. Sloane`
	EXTENSIONS	`More terms from Sean A. Irvine, Sep 25 2011`
	STATUS	`approved`

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Last modified September 11 06:30 EDT 2024. Contains 375814 sequences. (Running on oeis4.)