A305574 Number of primitive (1,1) pairs in the Fibonacci tree at depth 3n.

5, 2, 7, 30, 143, 728, 3876, 21318, 120175, 690690, 4032015, 23841480, 142498692, 859515920, 5225264024, 31983672534, 196947587823, 1219199353190, 7583142491925, 47365474641870, 296983176369495, 1868545312633440, 11793499763070480, 74650344244967400

Offset: 1

Author

Jeffrey Shallit, Jun 05 2018

Keywords

• nonn

References

• John Charles Saunders, Problems in Combinatorial and Analytic Number Theory, Ph. D. thesis, University of Waterloo, 2018.

Links

• Kevin G. Hare, and J. C. Saunders, On (a,b) Pairs in Random Fibonacci Sequences, Arxiv preprint arXiv:1608.03522 [math.NT], February 2018.

Crossrefs

Cf. A006013.

Programs

PARI

{a(n) = my(A); if( n<=1, 5*(n==1), A = O(x); for(k=1, n, A = x / (1 - A)^2); polcoeff(A, n))}; /* Michael Somos, Dec 10 2019 */

Extensions

More terms added and a(14) corrected by Michael Somos, Dec 10 2019