A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)).

2, 4, 16, 112, 448, 3136, 12544, 87808, 351232, 2458624, 9834496, 68841472, 275365888, 1927561216, 7710244864, 53971714048, 215886856192, 1511207993344, 6044831973376, 42313823813632, 169255295254528, 1184787066781696, 4739148267126784, 33174037869887488

Offset

1,1

Comments

From a(2) onwards, the digital root follows the pattern alternately 4,7,4,7,4,7,...

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,28).

Formula

a(1) = 2, a(2) = 4, a(3) = 16. a(2*n) = 4*a(2*n-1), a(2*n+1) = 7*a(2*n) for n > 1.

From Colin Barker, May 05 2016: (Start)

a(n) = 2^(-1+n)*(7^(1/2*(-3+n))*(2-2*(-1)^n + sqrt(7) + (-1)^n*sqrt(7))) for n > 1.

a(n) = 2^n*7^(n/2-1) for n > 1 and even.

a(n) = 2^(n+1)*7^((n-3)/2) for n > 1 and odd.

a(n) = 28*a(n-2) for n > 3.

G.f.: 2*x*(1+2*x-20*x^2) / (1-28*x^2).

(End)

E.g.f.: (-7 + 70*x + 7*cosh(2*Sqrt(7)*x) + 2*sqrt(7)*sinh(2*sqrt(7)*x))/49. - Ilya Gutkovskiy, May 05 2016

Mathematica

k = 2; Do[Print[k]; k *= Mod[Plus @@ IntegerDigits[k], 9], {n, 1, 30}] (* Ryan Propper, Oct 13 2005 *)
LinearRecurrence[{0, 28}, {2, 4, 16}, 30] (* Harvey P. Dale, Mar 17 2019 *)

Prog

(PARI) Vec(2*x*(1+2*x-20*x^2)/(1-28*x^2) + O(x^50)) \\ Colin Barker, May 05 2016

Crossrefs

Cf. A010888, A047892.

Sequence in context: A297009 A135249 A318154 * A047892 A275911 A334351

Adjacent sequences: A110362 A110363 A110364 * A110366 A110367 A110368

Keyword

base,easy,nonn

Author

Amarnath Murthy, Jul 24 2005

Extensions

More terms from Ryan Propper, Oct 13 2005

Name clarified by Robert Israel, May 05 2016

Status

approved