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

Author

Paul Barry, Apr 26 2004

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A076736.

Programs

Mathematica

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

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