login
A346629
Number of n-digit positive integers that are the product of two integers ending with 2.
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
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
KEYWORD
nonn,base,easy,less
AUTHOR
Stefano Spezia, Jul 25 2021
STATUS
approved