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A084264
Binomial transform of A084263.
2
1, 2, 7, 22, 64, 176, 464, 1184, 2944, 7168, 17152, 40448, 94208, 217088, 495616, 1122304, 2523136, 5636096, 12517376, 27656192, 60817408, 133169152, 290455552, 631242752, 1367343104, 2952790016, 6358564864, 13656653824, 29259464704
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
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
Sequence in context: A018039 A198888 A364539 * A333678 A088211 A071684
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2003
STATUS
approved