A346629 Number of n-digit positive integers that are the product of two integers ending with 2.

1, 4, 45, 450, 4500, 45000, 450000, 4500000, 45000000, 450000000, 4500000000, 45000000000, 450000000000, 4500000000000, 45000000000000, 450000000000000, 4500000000000000, 45000000000000000, 450000000000000000, 4500000000000000000, 45000000000000000000, 450000000000000000000

Offset: 1

Author

Stefano Spezia, Jul 25 2021

Keywords

• nonn
• base
• easy
• less

Comments

a(n) is the number of n-digit numbers in A139245.

After initial 1 or 2 values the same as A137233. - R. J. Mathar, Aug 23 2021

Links

• Index entries for linear recurrences with constant coefficients, signature (10).
• Index entries for sequences related to digits.

Crossrefs

Cf. A011557 (powers of 10), A017293 (positive integers ending with 2), A052268 (number of n-digit integers), A139245 (product of two integers ending with 2), A093143, A337855, A337856.

Cf. A137233.

Programs

Mathematica

LinearRecurrence[{10},{1,4,45},25]

Formula

O.g.f.: x*(1 - 6*x + 5*x^2)/(1 - 10*x).

E.g.f.: (9*exp(10*x) - 9 + 110*x - 50*x^2)/200.

a(n) = 10*a(n-1) for n > 3, with a(1) = 1, a(2) = 4 and a(3) = 45.

a(n) = 45*10^(n-3) for n > 2.

a(n) = 45*A011557(n-3) for n > 2.

Sum_{i=1..n} a(n) = A093143(n-1).