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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A004120 Expansion of (1 + x - x^5) / (1 - x)^3. (Formerly M3354) 10 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; 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 (3,-3,1) FORMULA a(n) = n*(n + 11)/2 - 5, n>=3. - R. J. Mathar, Mar 15 2011 a(n) = A302537(n-1), n>=3. - R. J. Mathar, Apr 24 2024 MAPLE 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: A010457 A244833 A331220 * A052118 A070470 A070469 Adjacent sequences: A004117 A004118 A004119 * A004121 A004122 A004123 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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