A134683 Expansion of 1+x*(2+3*x)/(1-4*x^2).

1, 2, 3, 8, 12, 32, 48, 128, 192, 512, 768, 2048, 3072, 8192, 12288, 32768, 49152, 131072, 196608, 524288, 786432, 2097152, 3145728, 8388608, 12582912, 33554432, 50331648, 134217728, 201326592, 536870912, 805306368, 2147483648, 3221225472

Offset: 0

Author

Paul Curtz, Jan 26 2008, Feb 09 2008

Keywords

• nonn
• easy

Comments

A002001 interleaved with A081294. Gary W. Adamson, Jul 08 2012

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4).

Crossrefs

Cf. A001045, A045623, A131577, A002001, A081294, A000302.

Programs

Maple

A134683 := proc(n)
    if n =0 then
        1 ;
    else
        -(-1)^n*A131577(n-1)+2*procname(n-1) ;
    end if;
end proc: # R. J. Mathar, Jul 22 2012

Mathematica

CoefficientList[Series[1 + x*(2 + 3*x)/(1 - 4*x^2), {x, 0, 32}], x] (* Amiram Eldar, Aug 18 2022 *)

Formula

a(n) = 2*a(n-1)-(-1)^n*A131577(n-1), n>0.

a(n) = 4*a(n-2), n>2. Gary W. Adamson, Jul 08 2012

a(n) = 2^(n-3)*(7-(-1)^n), n>0. - R. J. Mathar, Jul 22 2012

Sum_{n>=0} 1/a(n) = 19/9. - Amiram Eldar, Aug 18 2022

Extensions

Edited by N. J. A. Sloane, Feb 20 2008