A154383 Powers of 4 at even indices, two times powers of 4 at odd indices.

1, 0, 4, 2, 16, 8, 64, 32, 256, 128, 1024, 512, 4096, 2048, 16384, 8192, 65536, 32768, 262144, 131072, 1048576, 524288, 4194304, 2097152, 16777216, 8388608, 67108864, 33554432, 268435456, 134217728, 1073741824, 536870912, 4294967296, 2147483648, 17179869184, 8589934592, 68719476736, 34359738368, 274877906944

Offset: 0

Author

Paul Curtz, Jan 08 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4).

Programs

Magma

[1,0] cat [(5+3*(-1)^n)*2^(n-3): n in [2..40]]; // Vincenzo Librandi, Sep 16 2016

Mathematica

Join[{1, 0}, Table[(5 + 3*(-1)^n)*2^(n - 3), {n, 2, 20}]] (* G. C. Greubel, Sep 15 2016 *)

Formula

a(2n) = A131577(2n+1); a(2n+1) = A131577(2n) (Consecutive terms of A131577 swapped).

a(2n) = A000302(n); a(2n+1) = A000302(n)/2, n>0.

a(n) = 4*a(n-2), n>3.

a(2n+1) = a(2n)/2, n>0.

G.f.: (1 + 2*x^3)/((1-2*x)*(2*x+1)). - R. J. Mathar, May 21 2009

a(n) = (5 + 3*(-1)^n)*2^(n-3), n>1. - R. J. Mathar, May 21 2009

E.g.f.: (1/4)*(-2*x + sinh(2*x) + 4*cosh(2*x)). - G. C. Greubel, Sep 15 2016

Extensions

Edited by R. J. Mathar, May 21 2009