A084431 Expansion of g.f. (1 + 6*x + 5*x^2)/((1-2*x)*(1+2*x)).

1, 6, 9, 24, 36, 96, 144, 384, 576, 1536, 2304, 6144, 9216, 24576, 36864, 98304, 147456, 393216, 589824, 1572864, 2359296, 6291456, 9437184, 25165824, 37748736, 100663296, 150994944, 402653184, 603979776, 1610612736, 2415919104

Offset: 0

Author

Paul Barry, Jun 26 2003

Keywords

• nonn
• easy

Comments

Binomial transform is A085287.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4).

Crossrefs

Bisections are A002023 and A002063.

Cf. A085287.

Programs

Magma

[(-10*0^n-3*(-2)^n+21*2^n)/8: n in [0..30]]; // Vincenzo Librandi, Nov 16 2011

Mathematica

CoefficientList[Series[(1+6x+5x^2)/((1-2x)(1+2x)),{x,0,30}],x] (* or *) Join[{1},Flatten[NestList[4#&,{6,9},15]]] (* Harvey P. Dale, Nov 05 2011 *)

Formula

a(n) = (-10*0^n - 3*(-2)^n + 21*2^n)/8.

a(n) = 4*a(n-2), n > 1. - Harvey P. Dale, Nov 05 2011

E.g.f.: (9*cosh(2*x) + 12*sinh(2*x) - 5)/4. - Stefano Spezia, Sep 20 2023