0,1

Bode's law is that the average distance of the n-th planet from the sun is (4 + 3*floor(2^(n-1)))/10 astronomical units.

The Titius-Bode Law is a rough rule that predicts the spacing of the planets in the Solar System. The relationship was first pointed out by Johann Titius in 1766 and was formulated as a mathematical expression by J. E. Bode in 1778. It lead Bode to predict the existence of another planet between Mars and Jupiter in what is now called the asteroid belt. - Robert G. Wilson v, (rgwv@rgwv.com), Mar 19 2008

S. L. Jaki, "The Titius-Bode law: a strange bicentenary", Sky and Telescope, 43 (No. 5, May 1972), 280-281.

W. I. McLaughlin, ``Note on a tetranacci alternative to Bode's law,'' preprint, 1974.

J. R. Newman, The World of Mathematics, Vol. I, p. 221, 1956.

BBC Corp., Title?

M. Haynes and S. Churchman, Bode's Law

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

a(n)=2*a(n-1)-4, n>1.

A003461:=-(-4+5*z+3*z**2)/((2*z-1)*(z-1)); [Conjectured by S. Plouffe in his 1992 dissertation.] (This appears to be correct!)

Table[4 + 3 Floor[2^(n - 1)], {n, 0, 31}] (* Robert G. Wilson v, (rgwv@rgwv.com), Mar 19 2008 *)

(PARI) a(n)=4+3*floor(2^(n-1));

Cf. A061654.

First differences of A087009.

Sequence in context: A115288 A128429 A131500 this_sequence A023375 A119249 A071415

Adjacent sequences: A003458 A003459 A003460 this_sequence A003462 A003463 A003464

nonn,easy,nice

njas, W. I. McLaughlin

Description corrected by Michael Somos