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A163978 a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4. 3
3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152, 3145728 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Interleaving of A007283 and A000079 without initial terms 1 and 2.

Equals A029744 without first two terms. Agrees with A145751 for all terms listed there (up to 65536). Apparently equal to 3 followed by A090989.

Binomial transform is A078057 without initial 1, second binomial transform is A048580, third binomial transform is A163606, fourth binomial transform is A163604, fifth binomial transform is A163605.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

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

FORMULA

a(n) = A027383(n-1) + 2.

a(n) = A052955(n) + 1 for n >=1.

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

G.f.: x*(3+4*x)/(1-2*x^2).

E.g.f.: (1/2)*(4*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) - 4). - G. C. Greubel, Aug 24 2017

MATHEMATICA

Join[{3, 4}, LinearRecurrence[{0, 2}, {6, 8}, 50]]  (* or *) Table[(1/2)*(5 - (-1)^n)*2^((2*n - 1 + (-1)^n)/4) , {n, 1, 50}] (* G. C. Greubel, Aug 24 2017 *)

PROG

(MAGMA) [ n le 2 select n+2 else 2*Self(n-2): n in [1..41] ];

(PARI) x='x+O('x^50); Vec(x*(3+4*x)/(1-2*x^2)) \\ G. C. Greubel, Aug 24 2017

CROSSREFS

Cf. A007283 (3*2^n), A000079 (powers of 2), A029744, A145751, A090989, A078057, A048580, A163606, A163604, A163605, A027383, A052955.

Sequence in context: A299252 A299253 A063759 * A145751 A277099 A146566

Adjacent sequences:  A163975 A163976 A163977 * A163979 A163980 A163981

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Aug 07 2009

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)