OFFSET
0,2
COMMENTS
Also the number of matchings in the (n-1)-book graph. - Eric W. Weisstein, Sep 30 2017
LINKS
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Index entries for linear recurrences with constant coefficients, signature (6,-12,8)
FORMULA
E.g.f.: exp(x)cosh(x)+exp(2x)(x+x^2/2)
O.g.f.: (-1+x)*(1-3*x+4*x^2)/(-1+2*x)^3. - R. J. Mathar, Apr 02 2008
a(0)=1, a(1)=2, a(2)=7, a(3)=22, a(n)=6*a(n-1)-12*a(n-2)+8*a(n-3). - Harvey P. Dale, Mar 25 2012
a(n) = 2^(n-3)*(n^2+3*n+4) for n > 0. - Eric W. Weisstein, Sep 30 2017
MATHEMATICA
CoefficientList[Series[(-1 + x)(1 - 3 x + 4 x^2)/(-1 + 2 x)^3, {x, 0, 30}], x]
Join[{1}, LinearRecurrence[{6, -12, 8}, {2, 7, 22}, 30]]
Table[If[n == 0, 1, 2^(n - 3) (n^2 + 3 n + 4)], {n, 0, 20}] (* Eric W. Weisstein, Sep 30 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2003
STATUS
approved