A084264 Binomial transform of A084263.

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

Author

Paul Barry, May 31 2003

Keywords

• easy
• nonn
• changed

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)

Crossrefs

Cf. A084263.

Programs

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 *)

Formula

E.g.f.: exp(x)*cosh(x)+exp(2*x)*(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