A162255 - OEIS

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..42.

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A302853 A116626 A074323 * A164073 A286595 A348404

Adjacent sequences: A162252 A162253 A162254 * A162256 A162257 A162258

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jun 29 2009

EXTENSIONS

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

Corrected by Harvey P. Dale, Aug 28 2012

STATUS

approved