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A134683
Expansion of 1+x*(2+3*x)/(1-4*x^2).
5
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
0,2
COMMENTS
A002001 interleaved with A081294. Gary W. Adamson, Jul 08 2012
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
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jan 26 2008, Feb 09 2008
EXTENSIONS
Edited by N. J. A. Sloane, Feb 20 2008
STATUS
approved