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Number of zygodrome numbers in base-10 (A033023) with n or fewer digits.
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%I #61 Oct 01 2024 16:18:10

%S 0,9,18,108,279,1260,3780,15129,49158,185328,627759,2295720,7945560,

%T 28607049,100117098,357580548,1258634439,4476859380,15804569340,

%U 56096303769,198337427838,703204161768,2488241012319,8817078468240,31211247579120,110564953793289

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

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

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/zygodrome/">Zygodrome</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,-9).

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

%F From _Stefano Spezia_, Sep 07 2024: (Start)

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

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

%t LinearRecurrence[{1, 9}, {1, 10}, 26] - 1 (* _Amiram Eldar_, Sep 06 2024 *)

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

%Y Cf. A015445, A033023.

%K nonn,easy,base

%O 1,2

%A _Ruud H.G. van Tol_, Sep 06 2024