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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

N. J. A. Sloane

STATUS

approved

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Last modified October 23 01:36 EDT 2018. Contains 316518 sequences. (Running on oeis4.)