OFFSET
0,2
REFERENCES
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
John Riordan, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
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, 2, -3, 3, -1).
FORMULA
G.f.: x*(3 + 3*x + 2*x^2)/((1-x)^3*(1-x^3)).
[(8*n^3 + 27*n^2 + 21*n + 9)/18]
EXAMPLE
Examples for n=1 (i=internal, e=external node):
............................................e...e
...........e.e...........e.e.e.e..........e...i..
.......e.e..i...e.........i...i.........e...i....
........i.....i.........e...i.........e...i......
...........i..............i.............i........
...........e..............e.............e........
MAPLE
A001860:=(3+3*z+2*z**2)/(z**2+z+1)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
nn = 50; CoefficientList[Series[x*(3 + 3*x + 2*x^2)/((1 - x)^3*(1 - x^3)), {x, 0, nn}], x] (* T. D. Noe, Aug 10 2012 *)
PROG
(PARI) a(n)=(8*n^3+27*n^2+21*n+9)\18
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Additional comments from Michael Somos, Jun 06 2002
STATUS
approved