A087440 Expansion of (1-2x-3x^2)/((1-2x)(1-4x)).

1, 4, 13, 46, 172, 664, 2608, 10336, 41152, 164224, 656128, 2622976, 10488832, 41949184, 167784448, 671113216, 2684403712, 10737516544, 42949869568, 171799085056, 687195553792, 2748780642304, 10995119423488, 43980471402496

Offset: 0

Author

Paul Barry, Sep 03 2003

Keywords

• easy
• nonn

Comments

Binomial transform is A087439. Second binomial transform of A084221 (with extra leading 1).

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-8).

Crossrefs

Cf. A000217, A084221, A087439.

Programs

Mathematica

CoefficientList[Series[(1-2x-3x^2)/((1-2x)(1-4x)),{x,0,30}],x] (* or *) Join[{1},LinearRecurrence[{6,-8},{4,13},30]] (* Harvey P. Dale, Jan 18 2012 *)

Formula

a(n) = 5*4^n/8 + 3*2^n/4 - 3*0^n/8.

a(n) = 6*a(n-1) - 8*a(n-2), n>2. - Harvey P. Dale, Jan 18 2012

a(n) = A000217(2^n) + floor(A000217(2^(n-1))). - J. M. Bergot, May 03 2018