A114540 Number of correct decimal digits given by the n-th convergent to the golden ratio.

0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31, 31

Offset

0,6

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Golden Ratio

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

From Colin Barker, Oct 28 2015: (Start)

a(n) = a(n-1)+a(n-12)-a(n-13) for n>12.

G.f.: -x^3*(x^17-x^16-x^9-x^7-x^5-x^2-1)/(x^13-x^12-x+1).

(End)

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8}, 100] (* Harvey P. Dale, Jul 12 2020 *)

Prog

(PARI) concat(vector(3), Vec(-x^3*(x^17-x^16-x^9-x^7-x^5-x^2-1)/(x^13-x^12-x+1) + O(x^100))) \\ Colin Barker, Oct 28 2015

Crossrefs

Cf. A000045.

Sequence in context: A071824 A224921 A225370 * A183142 A121830 A020911

Adjacent sequences: A114537 A114538 A114539 * A114541 A114542 A114543

Keyword

nonn,base,less,easy

Author

Eric W. Weisstein, Dec 07 2005

Status

approved