A164587 a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.

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

Offset

1,2

Comments

Interleaving of A000079 and A000079 without initial terms 1, 2, 4.

Binomial transform is A048696. Second binomial transform is A164298.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 2).

Formula

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

G.f.: x*(1+8*x)/(1-2*x^2).

E.g.f.: 4*cosh(sqrt(2)*x) + (1/sqrt(2))*sinh(sqrt(2)*x) - 4. - G. C. Greubel, Aug 12 2017

Mathematica

CoefficientList[Series[(1 - x)/(1 - 10*x + 17*x^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2017 *)

Prog

(Magma) [ n le 2 select 7*n-6 else 2*Self(n-2): n in [1..41] ];
(PARI) x='x+O('x^50); Vec(x*(1+8*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 12 2017

Crossrefs

Equals A112032 without initial term 4.

Cf. A000079 (powers of 2), A048696, A164298.

Sequence in context: A167623 A040063 A196170 * A050096 A161593 A008866

Adjacent sequences: A164584 A164585 A164586 * A164588 A164589 A164590

Keyword

nonn

Author

Klaus Brockhaus, Aug 17 2009

Status

approved