OFFSET
0,2
REFERENCES
J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 12).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
J. Propp, Updated article
J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
FORMULA
G.f.: x*(2 - 5*x + x^2)/((1-x)^3*(1-2*x)). - Colin Barker, May 10 2012
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - Vincenzo Librandi, May 11 2012
EXAMPLE
G.f. = 2*x + 5*X^2 + 8*X^3 + 9*X^4 + 4*X^5 - 15*X^6 - 64*X^7 - 175*X^8 + ...
MATHEMATICA
Table[(2*n^2-2^n)/2, {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2010 *)
CoefficientList[Series[x*(2-5*x+x^2)/((1-x)^3*(1-2*x)), {x, 0, 40}], x] (* Vincenzo Librandi, May 11 2012 *)
LinearRecurrence[{5, -9, 7, -2}, {0, 2, 5, 8}, 40] (* Harvey P. Dale, Jan 14 2015 *)
PROG
(Magma) [(n-1)*(n+3)-2^n+4: n in [0..40]]; // Vincenzo Librandi, May 11 2012
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, May 28 2002
STATUS
approved