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A004120
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Expansion of (1+x-x^5 )/(1-x)^3.
(Formerly M3354)
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3
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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
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OFFSET
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0,2
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REFERENCES
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M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 109-111.
Solution to Problem 68-16, SIAM Rev. 12 (1970), 294-297.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Philippe Flajolet, BALLS AND URNS, ETC. A problem in submarine detection (solution to 68-16)
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1)
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FORMULA
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a(n) = n*(n+11)/2-5, n>=3. - R. J. Mathar, Mar 15 2011
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MAPLE
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(1+x-x^5)/(1-x)^3;
A004120:=(-1-z+z**5)/(z-1)**3; [Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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i=7; s=1; lst={s}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst [From 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]] (* From Harvey P. Dale, Oct 11 2011 *)
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PROG
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(MAGMA) [1, 4, 9], [n*(n+11)/2-5: n in [3..30]]; // Vincenzo Librandi, Oct 08 2011
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CROSSREFS
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Sequence in context: A126589 A010409 A010457 * A052118 A070470 A070469
Adjacent sequences: A004117 A004118 A004119 * A004121 A004122 A004123
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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