A213173 a(n) = 4^floor(n/2), Powers of 4 repeated.

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

Author

Philippe Deléham, Apr 14 2013

Keywords

• nonn
• easy

Comments

1, followed by A056450. - Joerg Arndt, Sep 17 2013

Binomial transform of A084567.

Unsigned version of A164111.

Also, number of walks of length n on the star S_4 = K_1,4 starting at a specific vertex of degree 1. - Sean A. Irvine, Jun 03 2025

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Sean A. Irvine, Walks on Graphs.
• Wikipedia, Star (graph theory)
• Index entries for linear recurrences with constant coefficients, signature (0,4).

Crossrefs

Cf. A000302, A056450, A164111.

Programs

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 *)

PARI

a(n)=4^(n\2) \\ Charles R Greathouse IV, Oct 03 2016

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