A337855 - OEIS

%I #29 Dec 10 2021 11:28:18

%S 0,2,18,180,1800,18000,180000,1800000,18000000,180000000,1800000000,

%T 18000000000,180000000000,1800000000000,18000000000000,

%U 180000000000000,1800000000000000,18000000000000000,180000000000000000,1800000000000000000,18000000000000000000,180000000000000000000

%N Number of n-digit positive integers that are the product of two integers ending with 5.

%C a(n) is the number of n-digit numbers in A053742.

%H Christian Krause, <a href="https://github.com/ckrause/loda">LODA, an assembly language, a computational model and a tool for mining integer sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%H <a href="/index/Di#digits">Index entries for sequences related to digits</a>.

%F O.g.f.: 2*(1 - x)*x^2/(1 - 10*x).

%F E.g.f.: (9*exp(10*x) - 9 - 90*x + 50*x^2)/500.

%F a(n) = 10*a(n-1) for n > 3 , with a(1) = 0, a(2) = 2 and a(3) = 18.

%F a(n) = 18*10^(n-3) for n > 2.

%F a(n) = 18*A011557(n - 3) for n > 2.

%F a(n) = 2*A052268(n - 2) for n > 2.

%F Sum_{i=2..n} a(n) = A093136(n - 1) for n > 1.

%F a(n) = 2*floor((k + 27*10^(n-2))/30), with 2 < k < 28. [This formula was found in the form k = 7 by _Christian Krause_'s LODA miner] - _Stefano Spezia_, Dec 06 2021

%t LinearRecurrence[{10},{0,0,2,18},22]

%Y Cf. A011557 (powers of 10), A052268 (number of n-digit integers), A053742 (product of two integers ending with 5), A093136, A337856.

%K nonn,easy,base

%O 1,2

%A _Stefano Spezia_, Sep 27 2020