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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved