A147595 a(n) is the number whose binary representation is A138144(n).

1, 3, 7, 15, 27, 51, 99, 195, 387, 771, 1539, 3075, 6147, 12291, 24579, 49155, 98307, 196611, 393219, 786435, 1572867, 3145731, 6291459, 12582915, 25165827, 50331651, 100663299, 201326595, 402653187, 805306371, 1610612739, 3221225475

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = A060013(n+2), n > 3. - R. J. Mathar, Feb 05 2010

a(n+4) = 3*(2^(n+2) + 1), n >= 0. - Brad Clardy, Apr 03 2013

From Colin Barker, Sep 15 2013: (Start)

a(n) = 3*(4 + 2^n)/4 for n>3.

a(n) = 3*a(n-1) - 2*a(n-2).

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

E.g.f.: (3/4)*(4*exp(x) + exp(2*x)) - (15/4) - 7*x/2 - 3*x^2/2 - x^3/3. - G. C. Greubel, Oct 25 2022

Mathematica

LinearRecurrence[{3, -2}, {1, 3, 7, 15, 27}, 40] (* Harvey P. Dale, Nov 30 2020 *)

Prog

(PARI) Vec(-x*(2*x^2-1)*(2*x^2+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Sep 15 2013
(Magma) [1, 3, 7] cat [3*(1+2^(n-2)): n in [4..40]]; // G. C. Greubel, Oct 25 2022
(SageMath) [1, 3, 7]+[3*(1+2^(n-2)) for n in range(4, 40)] # G. C. Greubel, Oct 25 2022

Crossrefs

Cf. A138144, A145641, A147537, A147538, A147539, A147540, A147590, A147596, A147597.

Sequence in context: A274008 A146742 A146425 * A378278 A147127 A146726

Adjacent sequences: A147592 A147593 A147594 * A147596 A147597 A147598

Keyword

base,easy,nonn

Author

Omar E. Pol, Nov 08 2008

Extensions

Extended by R. J. Mathar, Feb 05 2010

Status

approved