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a(n) = A006190(n) * A006190(n+2).
0

%I #15 Oct 15 2024 05:15:04

%S 10,99,1090,11880,129601,1413720,15421330,168220899,1835008570,

%T 20016873360,218350598401,2381839709040,25981886201050,

%U 283418908502499,3091626107326450,33724468272088440,367877524885646401,4012928305470021960,43774333835284595170,477504743882660524899,5208777848873981178730

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

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

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

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

%F Empirical g.f.: -x*(x-10) / ((x+1)*(x^2-11*x+1)). - _Colin Barker_, Oct 20 2013

%F 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

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

%Y Cf. A006190.

%K nonn

%O 1,1

%A _Gary W. Adamson_, Mar 16 2008