|
| |
|
|
A003411
|
|
Losing initial positions in game: two players alternate in removing >= 1 stones; last player wins; first player may not remove all stones; each move <= 3 times previous move.
(Formerly M0561)
|
|
2
| |
|
|
1, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 55, 76, 105, 145, 200, 276, 381, 526, 726, 1002, 1383, 1909, 2635, 3637, 5020, 6929, 9564, 13201, 18221, 25150, 34714, 47915, 66136, 91286, 126000, 173915, 240051, 331337, 457337, 631252, 871303, 1202640, 1659977
(list; graph; refs; listen; history; 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..1000
S. 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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
|
FORMULA
| a(n) = a(n-1) + a(n-4), n >= 5; G.f.: (1+x+x^2+x^3+x^4)/(1-x-x^4).
|
|
|
MAPLE
| A003411:=-(1+z+z**2+z**3+z**4)/(-1+z+z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
|
MATHEMATICA
| Join[{1}, LinearRecurrence[{1, 0, 0, 1}, {2, 3, 4, 6}, 80]] (* From Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *)
|
|
|
CROSSREFS
| Presumably equals A048590(n-3) - 3, n>3.
Sequence in context: A006683 A014213 A064323 * A034081 A064660 A066806
Adjacent sequences: A003408 A003409 A003410 * A003412 A003413 A003414
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy, Rodney W. Topor (rwt(AT)cit.gu.edu.au).
|
| |
|
|
