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Number of complete rulers with n segments.
4

%I #31 Oct 05 2024 21:05:21

%S 1,1,3,10,38,175,885,5101,32080,219569,1616882,12747354,106948772,

%T 950494868

%N Number of complete rulers with n segments.

%C For definitions, references and links related to complete rulers see A103294.

%C a(10) > 1616740 (contributions from rows of A103294 up to 39). - _Hugo Pfoertner_, Dec 16 2021

%H <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>

%F a(n) = Sum_{i=n..A004137(n+1)} T(i, n) where T is the A103294 triangle.

%e a(2)=3 counts the complete rulers with 2 segments, {[0,1,2],[0,1,3],[0,2,3]}.

%o (Fortran) ! Link to FORTRAN program given in A103295.

%Y Cf. A103301 (perfect rulers with n segments), A103299 (optimal rulers with n segments).

%Y Cf. A103294, A103295 (complete rulers of length n).

%K nonn,hard,more

%O 0,3

%A _Peter Luschny_, Feb 28 2005

%E a(9) from _Hugo Pfoertner_, Mar 17 2005

%E a(10)-a(11) from _Fausto A. C. Cariboni_, Mar 03 2022

%E a(12)-a(13) from _Fausto A. C. Cariboni_, Mar 08 2022