A162255 a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 2.

3, 2, 6, 4, 12, 8, 24, 16, 48, 32, 96, 64, 192, 128, 384, 256, 768, 512, 1536, 1024, 3072, 2048, 6144, 4096, 12288, 8192, 24576, 16384, 49152, 32768, 98304, 65536, 196608, 131072, 393216, 262144, 786432, 524288, 1572864, 1048576, 3145728, 2097152

Offset: 1

Author

Klaus Brockhaus, Jun 29 2009

Keywords

• nonn
• easy

Comments

Apparently a(n) = A074323(n+1). a(n) = A072946(n-1) for n > 1.

Partial sums are in A164053.

Binomial transform is A135532 without initial term -1. Second binomial transform is A161938.

Links

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

Crossrefs

Cf. A074323, A072946, A164053, A135532, A161938.

Programs

Mathematica

LinearRecurrence[{0,2},{3,2},50] (* Harvey P. Dale, Aug 28 2012 *)

PARI

m=42; u=concat([3, 2], vector(m-2)); for(n=3, m, u[n]=2*u[n-2]); u

Formula

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

G.f.: x*(3+2*x)/(1-2*x^2).

E.g.f.: cosh(sqrt(2)*x) + 3*sinh(sqrt(2)*x)/sqrt(2) - 1. - Stefano Spezia, May 26 2024

Extensions

G.f. corrected, comments and cross-references added by Klaus Brockhaus, Aug 08 2009

Corrected by Harvey P. Dale, Aug 28 2012