A094361 Pair-reversal of 1,4,4,16,16...

4, 1, 16, 4, 64, 16, 256, 64, 1024, 256, 4096, 1024, 16384, 4096, 65536, 16384, 262144, 65536, 1048576, 262144, 4194304, 1048576, 16777216, 4194304, 67108864, 16777216, 268435456, 67108864, 1073741824, 268435456, 4294967296, 1073741824

Offset

0,1

Links

Table of n, a(n) for n=0..31.

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

Formula

a(n) = k^(n/2)(1+k*sqrt(k)-(1-ksqrt(k))(-1)^n)/(2*sqrt(k)), the pair reversal of 1,k,k,k^2,k^2,k^3,k^3,... for k=4.

G.f.: (4+x)/(1-4*x^2).

a(n) = (9*2^n+7*(-2)^n)/4.

Recurrence: a(n) = 4a(n-2), a(0)=4, a(1)=1. - Ralf Stephan, Jul 17 2013

Mathematica

LinearRecurrence[{0, 4}, {4, 1}, 50] (* Harvey P. Dale, Apr 15 2017 *)

Crossrefs

Cf. A076736.

Sequence in context: A175844 A351434 A167343 * A187926 A285281 A285267

Adjacent sequences: A094358 A094359 A094360 * A094362 A094363 A094364

Keyword

nonn,easy

Author

Paul Barry, Apr 26 2004

Status

approved