A337855 Number of n-digit positive integers that are the product of two integers ending with 5.

0, 2, 18, 180, 1800, 18000, 180000, 1800000, 18000000, 180000000, 1800000000, 18000000000, 180000000000, 1800000000000, 18000000000000, 180000000000000, 1800000000000000, 18000000000000000, 180000000000000000, 1800000000000000000, 18000000000000000000, 180000000000000000000

Offset: 1

Author

Stefano Spezia, Sep 27 2020

Keywords

• nonn
• easy
• base

Comments

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

Links

• Christian Krause, LODA, an assembly language, a computational model and a tool for mining integer sequences
• Index entries for linear recurrences with constant coefficients, signature (10).
• Index entries for sequences related to digits.

Crossrefs

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

Programs

Mathematica

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

Formula

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

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

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

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

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

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

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

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