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

0,2

Comments

Also the number of matchings in the (n-1)-book graph. - Eric W. Weisstein, Sep 30 2017

Links

Table of n, a(n) for n=0..28.

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

Sequence in context: A018039 A198888 A364539 * A333678 A088211 A071684

Adjacent sequences: A084261 A084262 A084263 * A084265 A084266 A084267

Keyword

easy,nonn

Author

Paul Barry, May 31 2003

Status

approved