A374749 Number of zygodrome numbers in base-10 (A033023) with n or fewer digits.

0, 9, 18, 108, 279, 1260, 3780, 15129, 49158, 185328, 627759, 2295720, 7945560, 28607049, 100117098, 357580548, 1258634439, 4476859380, 15804569340, 56096303769, 198337427838, 703204161768, 2488241012319, 8817078468240, 31211247579120, 110564953793289

Offset: 1

Author

Ruud H.G. van Tol, Sep 06 2024

Keywords

• nonn
• easy
• base

References

• Maarten Looijen, Over getallen gesproken - Talking about numbers, Van Haren Publishing, 2018, page 513.

Links

• Giovanni Resta, Zygodrome.
• Index entries for linear recurrences with constant coefficients, signature (2,8,-9).

Crossrefs

Cf. A015445, A033023.

Programs

Mathematica

LinearRecurrence[{1, 9}, {1, 10}, 26] - 1 (* Amiram Eldar, Sep 06 2024 *)

PARI

a(n) = ([0, 1; 9, 1]^n)[2, 2] - 1;

Formula

a(n) = A015445(n) - 1.

From Stefano Spezia, Sep 07 2024: (Start)

G.f.: 9*x^2/((1 - x)*(1 - x - 9*x^2)).

E.g.f.: exp(x/2)*(cosh(sqrt(37)*x/2) + sinh(sqrt(37)*x/2)/sqrt(37)) - exp(x). (End)