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 A165808 Expansion of x*(403+2967*x+1047*x^2-x^3)/(1-x)^4. 10
 403, 4579, 16945, 41917, 83911, 147343, 236629, 356185, 510427, 703771, 940633, 1225429, 1562575, 1956487, 2411581, 2932273, 3522979, 4188115, 4932097, 5759341, 6674263, 7681279, 8784805, 9989257, 11299051, 12718603, 14252329, 15904645 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Old name was: As mentioned in short description of A165806, polynomials have the following unique property: let f(x) be a polynomial in x. Then f(x+k*f(x)) is congruent to 0 (mod(f(x)); here k belongs to N. The present case pertains to f(x) = x^3 + 2x + 11 when x is complex (2 + 3i). The quotient f(x+k*f(x))/f(x), for any given k, consists of two parts: a) a rational integer part and b) rational integer coefficient of sqrt(-1). This sequence pertains to a. LINKS G. C. Greubel, Table of n, a(n) for n = 1..5000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From R. J. Mathar, Sep 30 2009: (Start) a(n) = 1-13*n-321*n^2+736*n^3. G.f.: x*(403+2967*x+1047*x^2-x^3)/(1-x)^4. (End) From G. C. Greubel, Apr 08 2016: (Start) a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). E.g.f.: (1 -333*x - 318*x^2 + x^3)*exp(x). (end) EXAMPLE f(x)= x^3 + 2x + 11. When x = 2 + 3i, we get f(x) = -31 + 15i. x + f(x) = -29 + 18i. f(-29 + 18i) = 3752 + 39618i. When this value is divided by (-31 + 15i) we get 403 - 1083i; needless to say, PARI takes care of necessary rationalization. MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {403, 4579, 16945, 41917}, 100](* G. C. Greubel, Apr 08 2016 *) PROG (PARI) Vec((403+2967*x+1047*x^2-x^3)/(1-x)^4+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Cf. A165806, A165809. Sequence in context: A083815 A250893 A261857 * A283662 A097741 A117836 Adjacent sequences:  A165805 A165806 A165807 * A165809 A165810 A165811 KEYWORD nonn,easy AUTHOR A.K. Devaraj, Sep 29 2009 EXTENSIONS More terms from R. J. Mathar, Sep 30 2009 Edited by Jon E. Schoenfield, Dec 12 2013 STATUS approved

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)