A143095 (1, 2, 4, 8, ...) interleaved with (4, 8, 16, 32, ...).

1, 4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, 262144, 1048576, 524288, 2097152, 1048576, 4194304

Offset: 0

Author

Gary W. Adamson & Roger L. Bagula, Jul 23 2008

Keywords

• nonn
• easy

Comments

Partial sums are in A079360. a(n) = A076736(n+5). - Klaus Brockhaus, Jul 27 2009

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2).

Crossrefs

Cf. A048655.

Programs

Maple

seq(coeff(series((1+4*x)/(1-2*x^2), x, n+1), x, n), n = 0..45); # G. C. Greubel, Mar 13 2020

Mathematica

nn=30;With[{p=2^Range[0,nn]},Riffle[Take[p,nn-2],Drop[p,2]]] (* Harvey P. Dale, Oct 03 2011 *)

Maxima

A143095(n):=(5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2$
makelist(A143095(n),n,0,30); /* Martin Ettl, Nov 03 2012 */

PARI

for(n=0, 41, print1((5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2, ",")) \\ Klaus Brockhaus, Jul 27 2009

Sage

[(5 -3*(-1)^n)*2^((2*n-1+(-1)^n)/4)/2 for n in (0..45)] # G. C. Greubel, Mar 13 2020

Formula

Inverse binomial transform of A048655: (1, 5, 11, 27, 65, 157, ...).

a(n) = A135530(n+1). - R. J. Mathar, Aug 02 2008

From Klaus Brockhaus, Jul 27 2009: (Start)

a(n) = (5 - 3*(-1)^n) * 2^((2*n-1+(-1)^n)/4)/2.

a(n) = 2*a(n-2) for n > 1; a(0) = 1, a(1) = 4.

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

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

Extensions

More terms from Klaus Brockhaus, Jul 27 2009