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

1,2

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

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

Index entries for linear recurrences with constant coefficients, signature (10).

Index entries for sequences related to digits.

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).

Mathematica

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

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.

Sequence in context: A117644 A232729 A055602 * A073565 A039657 A114473

Adjacent sequences: A346626 A346627 A346628 * A346630 A346631 A346632

Keyword

nonn,base,easy,less

Author

Stefano Spezia, Jul 25 2021

Status

approved