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

1, 4, 13, 46, 172, 664, 2608, 10336, 41152, 164224, 656128, 2622976, 10488832, 41949184, 167784448, 671113216, 2684403712, 10737516544, 42949869568, 171799085056, 687195553792, 2748780642304, 10995119423488, 43980471402496, 175921873027072, 703687466942464, 2814749817438208

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..26.

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

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

E.g.f.: (5*exp(4*x) + 6*exp(2*x) - 3)/8. - Amiram Eldar, Jan 25 2026

Mathematica

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

Crossrefs

Cf. A000217, A084221, A087439.

Sequence in context: A026641 A149435 A149436 * A149437 A149438 A151448

Adjacent sequences: A087437 A087438 A087439 * A087441 A087442 A087443

Keyword

easy,nonn,changed

Author

Paul Barry, Sep 03 2003

Extensions

More terms from Amiram Eldar, Jan 25 2026

Status

approved