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 A004120 Expansion of (1 + x - x^5) / (1 - x)^3. (Formerly M3354) 9
 1, 4, 9, 16, 25, 35, 46, 58, 71, 85, 100, 116, 133, 151, 170, 190, 211, 233, 256, 280, 305, 331, 358, 386, 415, 445, 476, 508, 541, 575, 610, 646, 683, 721, 760, 800, 841, 883, 926, 970, 1015, 1061, 1108, 1156, 1205 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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 = 0..10000 D. R. Breach, Solution to Problem 68-16, SIAM Rev. 12 (1970), 294-297. D. R. Breach, Letter to N. J. A. Sloane, Jun 1980 Philippe Flajolet, Balls and urns, etc. A problem in submarine detection (solution to 68-16) M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 109-111. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (3,-3,1) FORMULA a(n) = n*(n + 11)/2 - 5, n>=3. - R. J. Mathar, Mar 15 2011 MAPLE (1+x-x^5)/(1-x)^3; A004120:=(-1-z+z**5)/(z-1)**3; # Simon Plouffe in his 1992 dissertation MATHEMATICA i=7; s=1; lst={s}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 30 2008 *) CoefficientList[Series[(1+x-x^5)/(1-x)^3, {x, 0, 50}], x] (* or *) Join[ {1, 4, 9}, LinearRecurrence[{3, -3, 1}, {16, 25, 35}, 50]] (* Harvey P. Dale, Oct 11 2011 *) PROG (MAGMA) [1, 4, 9], [n*(n+11)/2-5: n in [3..30]]; // Vincenzo Librandi, Oct 08 2011 (PARI) a(n)=if(n>2, (n^2+11*n)/2-5, (n+1)^2) \\ Charles R Greathouse IV, Sep 30 2015 CROSSREFS Sequence in context: A010409 A010457 A244833 * A052118 A070470 A070469 Adjacent sequences:  A004117 A004118 A004119 * A004121 A004122 A004123 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)