login
A213173
a(n) = 4^floor(n/2), Powers of 4 repeated.
6
1, 1, 4, 4, 16, 16, 64, 64, 256, 256, 1024, 1024, 4096, 4096, 16384, 16384, 65536, 65536, 262144, 262144, 1048576, 1048576, 4194304, 4194304, 16777216, 16777216, 67108864, 67108864, 268435456, 268435456, 1073741824, 1073741824, 4294967296, 4294967296
OFFSET
0,3
COMMENTS
1, followed by A056450. - Joerg Arndt, Sep 17 2013
Binomial transform of A084567.
Unsigned version of A164111.
FORMULA
O.g.f.: (1+x)/(1-4*x^2).
a(n) = A016116(n)^2.
a(n) = 4*a(n-2) with a(0) = a(1) = 1.
a(n) = a(n-1)*a(n-2)/a(n-3) = 4^A004526(n).
a(n) = sum(A152815(n,k)*3^k, 0<=k<=n). - Philippe Deléham, Apr 22 2013
MATHEMATICA
LinearRecurrence[{0, 4}, {1, 1}, 40] (* T. D. Noe, Apr 17 2013 *)
CoefficientList[Series[(1 + x)/(1 - 4*x^2), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2017 *)
With[{p4=4^Range[0, 30]}, Riffle[p4, p4]] (* Harvey P. Dale, Mar 17 2022 *)
PROG
(PARI) a(n)=4^(n\2) \\ Charles R Greathouse IV, Oct 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Apr 14 2013
STATUS
approved