A071099 a(n) = (n-1)*(n+3) - 2^n + 4.

0, 2, 5, 8, 9, 4, -15, -64, -175, -412, -903, -1904, -3927, -7996, -16159, -32512, -65247, -130748, -261783, -523888, -1048135, -2096668, -4193775, -8388032, -16776591, -33553756, -67108135, -134216944, -268434615, -536870012, -1073740863, -2147482624, -4294966207, -8589933436, -17179867959

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

Sequence in context: A131716 A011279 A185094 * A078001 A072955 A288730

Adjacent sequences: A071096 A071097 A071098 * A071100 A071101 A071102

Keyword

sign,easy

Author

N. J. A. Sloane, May 28 2002

Status

approved