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

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A348685 A110485 A240988 * A022664 A316463 A167784

Adjacent sequences: A154380 A154381 A154382 * A154384 A154385 A154386

Keyword

nonn,easy

Author

Paul Curtz, Jan 08 2009

Extensions

Edited by R. J. Mathar, May 21 2009

Status

approved