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

1,2

Comments

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

Links

Table of n, a(n) for n=1..22.

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.

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

Mathematica

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

Crossrefs

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

Sequence in context: A132306 A264196 A214768 * A099044 A161122 A019581

Adjacent sequences: A337852 A337853 A337854 * A337856 A337857 A337858

Keyword

nonn,easy,base

Author

Stefano Spezia, Sep 27 2020

Status

approved