A138365 a(n) = A006190(n) * A006190(n+2).

10, 99, 1090, 11880, 129601, 1413720, 15421330, 168220899, 1835008570, 20016873360, 218350598401, 2381839709040, 25981886201050, 283418908502499, 3091626107326450, 33724468272088440, 367877524885646401, 4012928305470021960, 43774333835284595170, 477504743882660524899, 5208777848873981178730

Offset: 1

Author

Gary W. Adamson, Mar 16 2008

Keywords

• nonn

Comments

1/3 = 3/10 + 3/99 + 3/1090, + 3/11880 + ..., = 3/(1*10) + 3/(3*33) + 3/(10*109) + 3/(33*360) + ...

Odd n terms == 1 mod 9; even n terms == 0 mod 9

Examples

			a(3) = A006190(3) * A006190(5) = 10 * 109 = 1090.
		

Crossrefs

Cf. A006190.

Formula

a(n) = A006190(n) * A006190(n+2).

Empirical g.f.: -x*(x-10) / ((x+1)*(x^2-11*x+1)). - Colin Barker, Oct 20 2013

For n >= 4, a(n) = 10*a(n-1) + 10*a(n-2) - a(n-3); from this it follows that the conjectured generating function is correct. - Sela Fried, Oct 14 2024