

A035337


Third column of Wythoff array.


13



3, 11, 16, 24, 32, 37, 45, 50, 58, 66, 71, 79, 87, 92, 100, 105, 113, 121, 126, 134, 139, 147, 155, 160, 168, 176, 181, 189, 194, 202, 210, 215, 223, 231, 236, 244, 249, 257, 265, 270, 278, 283, 291, 299, 304, 312
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OFFSET

0,1


COMMENTS

Also, positions of 3's in A139764, the smallest term in Zeckendorf representation of n.  John W. Layman, Aug 25 2011
The formula a(n) = 3*A003622(n)n+1 = 3AA(n)n+1 conjectured by Layman below is correct, since it is well known that AA(n)+1 = B(n) = A(n)+n, where B = A001950, and so 3AA(n)n+1 = 3B(n)n2 = 3A(n)+2n2.  Michel Dekking, Aug 31 2017


LINKS

Table of n, a(n) for n=0..45.
J. H. Conway and N. J. A. Sloane, Notes on the ParaFibonacci and related sequences
C. Kimberling, Complementary equations and Wythoff Sequences, JIS 11 (2008) 08.3.3
N. J. A. Sloane, Classic Sequences


FORMULA

a(n) = F(4)A(n)+F(3)(n1) = 3A(n)+2n2, where A = A000201 and F = A000045.  Michel Dekking, Aug 31 2017
It appears that a(n) = 3*A003622(n)  n + 1.  John W. Layman, Aug 25 2011


MAPLE

t := (1+sqrt(5))/2 ; [ seq(3*floor((n+1)*t)+2*n, n=0..80) ];


MATHEMATICA

Table[3 Floor[n GoldenRatio] + 2 n  2, {n, 46}] (* Michael De Vlieger, Aug 31 2017 *)


PROG

(Python)
from sympy import floor
from mpmath import phi
def a(n): return 3*floor((n + 1)*phi) + 2*n # Indranil Ghosh, Jun 10 2017
(PARI) a(n) = 2*n + 3*floor((1+sqrt(5))*(n+1)/2); \\ Altug Alkan, Sep 18 2017


CROSSREFS

Cf. A139764.
Let A = A000201, B = A001950. Then AA = A003622, AB = A003623, BA = A035336, BB = A101864. The eight triples AAA, AAB, ..., BBB are A134859, A134860, A035337, A134862, A134861, A134863, A035338, A134864, resp.
Sequence in context: A158507 A030765 A198515 * A029500 A243770 A298701
Adjacent sequences: A035334 A035335 A035336 * A035338 A035339 A035340


KEYWORD

nonn


AUTHOR

N. J. A. Sloane and J. H. Conway


STATUS

approved



